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 Inequalities/193264: Could someone help me with this? This is the problem to solve with set builder notation. I don't know what set builder notation is. 5[5m-(m+4)]>-8(m-2) Thank-you very much.1 solutions Answer 145080 by jim_thompson5910(28550)   on 2009-04-26 22:38:40 (Show Source): You can put this solution on YOUR website! ... Start with the given inequality. ... Distribute. Distribute again. Combine like terms on the left side. Add to both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is which in set-builder notation is
 Linear-systems/193227: Solve by the elimination method. 0.3x-0.2y=4 0.2x+0.3y=5/23 1 solutions Answer 145055 by jim_thompson5910(28550)   on 2009-04-26 18:48:24 (Show Source): You can put this solution on YOUR website! Start with the first equation. Multiply EVERY term by 10 to make every number a whole number. -------------------------- Move onto the second equation. Multiply EVERY term by the LCD 23 to clear out the fraction. Multiply and simplify Multiply EVERY term by 10 to make every number a whole number. So we have the system of equations: Multiply the both sides of the first equation by 69. Distribute and multiply. Multiply the both sides of the second equation by 2. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ========================================================================= Answer: So the solutions are and which form the ordered pair
test/193222: how do you factor this problem?
2a^2 + 7a - 4.
1 solutions

Answer 145054 by jim_thompson5910(28550)   on 2009-04-26 18:33:27 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,4,8
-1,-2,-4,-8

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-8)
2*(-4)
(-1)*(8)
(-2)*(4)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1-81+(-8)=-7
2-42+(-4)=-2
-18-1+8=7
-24-2+4=2

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

---------------------------------------------

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

 Exponential-and-logarithmic-functions/193213: what i mean is how i solve this without a calculator, because i dont know how to solve for X on the equation so what do i do, I know that X=3 when the equation is but i need to know why1 solutions Answer 145051 by jim_thompson5910(28550)   on 2009-04-26 17:34:24 (Show Source): You can put this solution on YOUR website!It turns out that anything raised to the one half power is equivalent to taking the square root. In other words So... So the solution is
 Linear-equations/193200: need to graph and find y intercept y=1/5x1 solutions Answer 145040 by jim_thompson5910(28550)   on 2009-04-26 16:44:22 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is note: really looks like Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 1 and the run is 5. This means that to go from point to point, we can go up 1 and over 5 So starting at , go up 1 unit and to the right 5 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Quadratic-relations-and-conic-sections/193197: How do i do question number 77 on 10.3 Write an equation of the line that is tangent to the circle at that point. 77) x2+ y2= 244; (-10, -12) Please explain the steps..1 solutions Answer 145039 by jim_thompson5910(28550)   on 2009-04-26 16:42:39 (Show Source): You can put this solution on YOUR website!To find the tangent line, we need the slope of the tangent line. To find that, we first need the first derivative of "y": ... Start with the given equation. ... Derive both sides with respect to "x" ... Derive the left and right sides. Note: remember, y is a function of "x", so use the chain rule. ... Subtract 2x from both sides. ... Divide both sides by 2y. ... Reduce So the slope of any tangent line at the point (x,y) (on the circle) is Now just plug in the values and to find the tangent slope at (-10,-12): ... Reduce So the slope of the tangent line is Now let's find the equation of the line that has a slope of and goes through (-10, -12): If you want to find the equation of line with a given a slope of which goes through the point (-10,-12), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Rewrite as Distribute Multiply and to get Subtract 12 from both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the tangent line is
 Graphs/193194: Can someone please help me. I am pulling my hair out. What does this question mean and how do you do it? What does this thing look like? Create a graph with precisely two odd vertices and two even vertices. State which of your vertices are even and which are odd. Use a dot and letter to mark each vertex. 1 solutions Answer 145037 by jim_thompson5910(28550)   on 2009-04-26 16:14:30 (Show Source): You can put this solution on YOUR website!Here's some terminology: Vertex: A point representing a location (city, town, etc...). In general, what the vertex represents isn't important. Edge: A line connecting two vertices (plural for vertex) Odd Vertex: A vertex with an odd number of edges connecting to it Even Vertex: A vertex with an even number of edges connecting to it So here's one way to draw the graph: Take note that... Vertex A: even vertex with 2 edges connecting to it Vertex B: odd vertex with 3 edges connecting to it Vertex C: even vertex with 2 edges connecting to it Vertex D: odd vertex with 3 edges connecting to it
 Pythagorean-theorem/193186: I looked at the solution for question #193175: A diagonal walk through a rectangular rose garden 18 meters by 24 meters can be built at $12 per linear meter. How much will the walk cost? But I was unable to figure out what ankor was talking about. I am not as versed in using a calculator as some are and did not understand. Can someone help please. 1 solutions Answer 145032 by jim_thompson5910(28550) on 2009-04-26 15:44:59 (Show Source): You can put this solution on YOUR website!First, we need to find the length of diagonal: If we cut the garden in half along the diagonal, we'll have this triangle set up (where "x" is the length of the diagonal): Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse. Since the legs are and this means that and Also, since the hypotenuse is , this means that . Start with the Pythagorean theorem. Plug in , , Square to get . Square to get . Combine like terms. Rearrange the equation. Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense). Take the square root of 900 to get 30. So the diagonal is 30 meters long. Now just multiply the length of the diagonal by the cost per linear meter to get: So it will cost$360 to build the diagonal walkway.
 Linear-systems/193189: Two angles are complimentary. The sum of the measure of the first angle and helf the second angle is 68 degrees. Find the measures of the angles.1 solutions Answer 145027 by jim_thompson5910(28550)   on 2009-04-26 15:34:21 (Show Source): You can put this solution on YOUR website!"Two angles are complimentary." translates to . Solve for "y" to get "The sum of the measure of the first angle and helf the second angle is 68 degrees." translates to Start with the second equation. Plug in Distribute Subtract 45 from both sides. Combine like terms. Multiply both sides by 2. Multiply ------------------------ Go back to the first equation Plug in Subtract So the solutions are and which means that the first and second angles are 46 and 44 degrees.
 Radicals/193166: sqrt(4x-5)=sqrt(x+9) 1 solutions Answer 145006 by jim_thompson5910(28550)   on 2009-04-26 12:50:06 (Show Source): You can put this solution on YOUR website! Start with the given equation. Square both sides Square the square roots to eliminate them Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is which approximates to .
 Pythagorean-theorem/193132: Liz is flying a kite. she let out 80 ft of string and attached the string to a stake in the ground, the kite is now directly above her brother mike who is 32 ft away from liz. find the height of the kite to the nearest foot. 1 solutions Answer 144974 by jim_thompson5910(28550)   on 2009-04-26 01:20:24 (Show Source): You can put this solution on YOUR website! First, let's draw a picture: We can see that a triangle forms where the legs are "x" and 32 ft with a hypotenuse of 80 ft. To find the unknown length of the leg "x", we need to use the Pythagorean Theorem Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse. Since the legs are and this means that and Also, since the hypotenuse is , this means that . Start with the Pythagorean theorem. Plug in , , Square to get . Square to get . Subtract from both sides. Combine like terms. Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense). Evaluate the square root (using a calculator). Note: this value is approximate Now round to the nearest whole number to get So the kite is about 73 ft above Mike's head.
 Rational-functions/193129: This question is from textbook Rewrite with rational exponents: square root of 171 solutions Answer 144969 by jim_thompson5910(28550)   on 2009-04-26 01:02:42 (Show Source): You can put this solution on YOUR website!Since the square root is really a "second root", this means that . Since the square root is so commonly used, we've dropped the 2 (as we know that we're dealing with a square root when no number is present) So Now, recall that In this case, , , and . So... We can simplify further to get So the answer is
 Radicals/193112: Simplify: 3rd order radical of 432x^8 (instead of square root it is the cube root) How is this simplified. is this how you set it up: 3 over the SR of 423x^8 ? I am not really sue where to go from here. Do I find the cube root of 423 first the mulitiply by power of 8 or the other way around? thank very much for all your help on this. this prolbem is from an online homework problem. it is not out of a book. I am currently in a Algebra II class on Univeristy Of Phoenix. thank you 1 solutions Answer 144950 by jim_thompson5910(28550)   on 2009-04-25 20:54:05 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor 432 into . Note: 216 is a perfect cube Factor into . Break up the root. Take the cube root of 216 to get 6 Take the cube root of to get Rearrange the terms and multiply So
 Equations/193107: I have problems solving the following equation Problem : 19^(1-x)= 12 In terms of log or ln or correct to four decimal places1 solutions Answer 144947 by jim_thompson5910(28550)   on 2009-04-25 19:40:13 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take the log base 10 of both sides Pull down the exponent Divide both sides by . Use the change of base formula to rewrite the right side Subtract 1 from both sides. Multiply EVERY term by -1 to isolate "x" So the solution is which approximates to
Polynomials-and-rational-expressions/193101: 40x^2-48x-88
1 solutions

Answer 144946 by jim_thompson5910(28550)   on 2009-04-25 19:36:18 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF

Now let's focus on the inner expression

------------------------------------------------------------

Looking at we can see that the first term is and the last term is where the coefficients are 5 and -11 respectively.

Now multiply the first coefficient 5 and the last coefficient -11 to get -55. Now what two numbers multiply to -55 and add to the middle coefficient -6? Let's list all of the factors of -55:

Factors of -55:
1,5,11,55

-1,-5,-11,-55 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -55
(1)*(-55)
(5)*(-11)
(-1)*(55)
(-5)*(11)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6

First NumberSecond NumberSum
1-551+(-55)=-54
5-115+(-11)=-6
-155-1+55=54
-511-5+11=6

From this list we can see that 5 and -11 add up to -6 and multiply to -55

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

------------------------------------------------------------

So our expression goes from and factors further to

------------------

So completely factors to

 Finance/193100: I need help trying to solve this problem, Thanks Problem : What is the amount P that must be invested at interest rate 5.5% compounded daily to obtain the balance of A =$150000 in t years. t = 1 P=? t= 10 P=? Given is the interest rate formula A=P(1+(r/n))^nt Any help with this question will be greatly appreciated, thanks. 1 solutions Answer 144944 by jim_thompson5910(28550) on 2009-04-25 18:49:36 (Show Source): You can put this solution on YOUR website! Start with the compound interest formula Plug in , (this is the decimal form of 5.5% interest), and Divide. Note: this value is approximate. So all future calculations will be approximate. Add Divide both sides by to isolate "P". Rearrange the equation Now simply plug in the given values of "t" to find P: t=1: Start with the given equation. Plug in Multiply Raise 1.0001507 to the 365th power to get 1.0565420 Divide So if you want to have$150,000 in the account in 1 year, you need to invest about \$141,972.59 in the account. I'll let you do the other value of t (it will follow the same procedure).
 Linear-equations/193089: Find the domain of each function f(x)=____8____ 2x+31 solutions Answer 144937 by jim_thompson5910(28550)   on 2009-04-25 16:59:04 (Show Source): You can put this solution on YOUR website!Since you CANNOT divide by zero, this means that we must take out values of x out of the domain that make the denominator equal to zero Set the denominator equal to zero. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . So when the denominator is zero. So we must make the restriction that So the domain is x can be any real number BUT
 Square-cubic-other-roots/193083: Simplify sqrt(36)/sqrt(64)1 solutions Answer 144924 by jim_thompson5910(28550)   on 2009-04-25 14:20:51 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite each number as a square of a whole number Take the square root of the squares (to eliminate the squares). Reduce So
 Quadratic_Equations/193074: 2x^2-3x+2a=0 the 2a is giving me trouble1 solutions Answer 144923 by jim_thompson5910(28550)   on 2009-04-25 14:13:54 (Show Source): You can put this solution on YOUR website!I'm assuming that you want to solve for "x" right? Start with the quadratic formula Plug in , , and . Note: there are two different "a" terms here... Negate to get . Square to get . Multiply to get Multiply 2 and 2 to get 4 or Break up the "plus/minus" to form two equations. So the solutions are or If we knew the value of "a", then we could continue simplifying.
 Inequalities/193080: Solve (4/5)(2x-1)>121 solutions Answer 144922 by jim_thompson5910(28550)   on 2009-04-25 14:04:31 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Multiply both sides by 5 Multiply. Distribute. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is The answer in set-builder notation is
 Inequalities/193079: Graph 8x-7<=15+y1 solutions Answer 144921 by jim_thompson5910(28550)   on 2009-04-25 14:03:54 (Show Source): You can put this solution on YOUR website! Start with the given inequality Subtract y from both sides. Add 7 to both sides. Combine like terms. Now let's graph In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify Since this inequality is true, we simply shade the entire region that contains (0,0) Graph of with the boundary (which is the line in red) and the shaded region (in green)
 Inequalities/193078: Graph 2x+3y<=61 solutions Answer 144920 by jim_thompson5910(28550)   on 2009-04-25 14:03:15 (Show Source): You can put this solution on YOUR website!In order to graph , we need to graph the equation (just replace the inequality sign with an equal sign). So lets graph the line (note: if you need help with graphing, check out this solver) graph of Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,0) into the inequality Plug in and Simplify Since this inequality is true, we simply shade the entire region that contains (0,0) Graph of with the boundary (which is the line in red) and the shaded region (in green)
 Inequalities/193076: Solve (2x-3)/6<=-9 or (2x-3)/6>=11 solutions Answer 144919 by jim_thompson5910(28550)   on 2009-04-25 14:02:28 (Show Source): You can put this solution on YOUR website!Let's solve the first inequality : Start with the first inequality. Multiply both sides by 6. Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . --------------------------------------------------------------------- Now let's solve the second inequality : Start with the second inequality. Multiply both sides by 6. Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . So our answer is or Which in set-builder notation looks like
 Square-cubic-other-roots/193070: Please help me. I do not understand the exponent fully and how to solve and simplify this. I could use any help in this . Thank you so much!! :) SR(300x^4)/SR(5x) does this mean I need to find: the sr of 300 that is multiplied 4 time to get 300? and 5 is as low of a sr and you can get correct? i am lost as to where to go after this? this problem is not from a text book. It is from a homework problem from an online math course wiht University of Pheonix Math 209/Algerbra II thank again for all your help Sincerely, Sherri1 solutions Answer 144916 by jim_thompson5910(28550)   on 2009-04-25 13:45:06 (Show Source): You can put this solution on YOUR website! Start with the given expression. Combine the roots. Divide to get Factor into Factor into Break up the square root using the identity . Take the square root of to get . Take the square root of to get . Rearrange and combine the terms. ================================================== Answer: So simplifies to In other words, where
 Quadratic_Equations/193037: State whether the following statements are true or false and justify your answer. a.a(x-alpha)(x-beta) can always be expressed as a(x-h)^2+k b.a(x-h)^2+k can always be expressed as a(x-alpha)(x-beta).1 solutions Answer 144915 by jim_thompson5910(28550)   on 2009-04-25 13:41:34 (Show Source): You can put this solution on YOUR website!a) The given statement is true, here's why... ... Start with the given expression. ... FOIL ... Combine like terms. Let and to get ... Take half of "b" and square it to get . Add AND subtract this inside the parenthesis. ... Factor the first three terms in the parenthesis ... Distribute Let to get Let to get So for ANY expression of the form you can rewrite it as ============================================================ b) The given statement is false (if you are only restricted to factor over the reals) Here's a counter-example: Let , , and . So the general expression becomes ----------- Start with the given expression. FOIL Combine like terms. Since you CANNOT factor over the reals, this means that CANNOT be written in the form of Note: if you are allowed to factor over the complex numbers, then you can rewrite into
Polynomials-and-rational-expressions/193068: THE FACTOR THEOREM
Factor P(x) = 6x^3 + 31x^2 + 4x -5 given that x+5 is one factor.
Factor R(x) = x^4 -2x3 + x^2 -4, given that x+1 and x-2 are factors.
1 solutions

Answer 144914 by jim_thompson5910(28550)   on 2009-04-25 13:20:59 (Show Source):
You can put this solution on YOUR website!
# 1

To factor , we can use synthetic division

First, let's find our test zero:

Set the given factor equal to zero

Solve for x.

so our test zero is -5

Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of to the right of the test zero.
 -5 | 6 31 4 -5 |

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 6)
 -5 | 6 31 4 -5 | 6

Multiply -5 by 6 and place the product (which is -30) right underneath the second coefficient (which is 31)
 -5 | 6 31 4 -5 | -30 6

Add -30 and 31 to get 1. Place the sum right underneath -30.
 -5 | 6 31 4 -5 | -30 6 1

Multiply -5 by 1 and place the product (which is -5) right underneath the third coefficient (which is 4)
 -5 | 6 31 4 -5 | -30 -5 6 1

Add -5 and 4 to get -1. Place the sum right underneath -5.
 -5 | 6 31 4 -5 | -30 -5 6 1 -1

Multiply -5 by -1 and place the product (which is 5) right underneath the fourth coefficient (which is -5)
 -5 | 6 31 4 -5 | -30 -5 5 6 1 -1

Add 5 and -5 to get 0. Place the sum right underneath 5.
 -5 | 6 31 4 -5 | -30 -5 5 6 1 -1 0

Since the last column adds to zero, we have a remainder of zero. This means is a factor of

Now lets look at the bottom row of coefficients:

The first 3 coefficients (6,1,-1) form the quotient

So factors to

In other words,

I'll let you continue the factorization....

# 2

First lets find our test zero:

Set the denominator equal to zero

Solve for x.

so our test zero is -1

Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of to the right of the test zero.(note: remember if a polynomial goes from to there is a zero coefficient for . This is simply because really looks like
 -1 | 1 -2 1 0 -4 |

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
 -1 | 1 -2 1 0 -4 | 1

Multiply -1 by 1 and place the product (which is -1) right underneath the second coefficient (which is -2)
 -1 | 1 -2 1 0 -4 | -1 1

Add -1 and -2 to get -3. Place the sum right underneath -1.
 -1 | 1 -2 1 0 -4 | -1 1 -3

Multiply -1 by -3 and place the product (which is 3) right underneath the third coefficient (which is 1)
 -1 | 1 -2 1 0 -4 | -1 3 1 -3

Add 3 and 1 to get 4. Place the sum right underneath 3.
 -1 | 1 -2 1 0 -4 | -1 3 1 -3 4

Multiply -1 by 4 and place the product (which is -4) right underneath the fourth coefficient (which is 0)
 -1 | 1 -2 1 0 -4 | -1 3 -4 1 -3 4

Add -4 and 0 to get -4. Place the sum right underneath -4.
 -1 | 1 -2 1 0 -4 | -1 3 -4 1 -3 4 -4

Multiply -1 by -4 and place the product (which is 4) right underneath the fifth coefficient (which is -4)
 -1 | 1 -2 1 0 -4 | -1 3 -4 4 1 -3 4 -4

Add 4 and -4 to get 0. Place the sum right underneath 4.
 -1 | 1 -2 1 0 -4 | -1 3 -4 4 1 -3 4 -4 0

Since the last column adds to zero, we have a remainder of zero. This means is a factor of

Now lets look at the bottom row of coefficients:

The first 4 coefficients (1,-3,4,-4) form the quotient

So factors to

In other words,

Now let's use the factor to factor

First lets find our test zero:

Set the denominator equal to zero

Solve for x.

so our test zero is 2

Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of to the right of the test zero.
 2 | 1 -3 4 -4 |

Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 1)
 2 | 1 -3 4 -4 | 1

Multiply 2 by 1 and place the product (which is 2) right underneath the second coefficient (which is -3)
 2 | 1 -3 4 -4 | 2 1

Add 2 and -3 to get -1. Place the sum right underneath 2.
 2 | 1 -3 4 -4 | 2 1 -1

Multiply 2 by -1 and place the product (which is -2) right underneath the third coefficient (which is 4)
 2 | 1 -3 4 -4 | 2 -2 1 -1

Add -2 and 4 to get 2. Place the sum right underneath -2.
 2 | 1 -3 4 -4 | 2 -2 1 -1 2

Multiply 2 by 2 and place the product (which is 4) right underneath the fourth coefficient (which is -4)
 2 | 1 -3 4 -4 | 2 -2 4 1 -1 2

Add 4 and -4 to get 0. Place the sum right underneath 4.
 2 | 1 -3 4 -4 | 2 -2 4 1 -1 2 0

Since the last column adds to zero, we have a remainder of zero. This means is a factor of

Now lets look at the bottom row of coefficients:

The first 3 coefficients (1,-1,2) form the quotient

So

Basically factors to

So

This means that then becomes

So all you have to do now is factor (I'll let you do that)

 Graphs/193065: I know this is a lot to ask but I really need some help. I don't get this at all. 1. Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city. a) The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation. b) The sales representative later indicates that there are 3 times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in part a. c) Use the equations from part a and b of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem. d) What are the intercepts of the equation from part a of this problem? What are the intercepts from part b of this problem? Where would the lines intersect if you solved the system by graphing? Thank-you for any help you can be, I'd be grateful.1 solutions Answer 144913 by jim_thompson5910(28550)   on 2009-04-25 13:13:09 (Show Source): You can put this solution on YOUR website!This question has been answered many times before. Check out this solution
 Proofs/193061: Construct Conditional Proofs 1. P → Q 2. (P • Q) → R 3. P → (R → S) 4. (R • S) → T / P → T (Hint: This is a long proof!) 1 solutions Answer 144910 by jim_thompson5910(28550)   on 2009-04-25 13:03:04 (Show Source): You can put this solution on YOUR website!1. P → Q 2. (P • Q) → R 3. P → (R → S) 4. (R • S) → T / P → T ----------------------- 5. P Assumption 6. Q 1,5 Modus Ponens 7. P • Q 5,6 Conjunction 8. R 2,7 Modus Ponens 9. P • R 5,8 Conjunction 10. (P • R) -> S 3 Exportation 11. S 10,9 Modus Ponens 12. R • S 8,11 Conjunction 13. T 4,12 Modus Ponens 14. P -> T 5,13 Conditional Proof 
 Proofs/193062: Construct Conditional Proofs 1. (A v B) → (C • D) / A → C 1 solutions Answer 144907 by jim_thompson5910(28550)   on 2009-04-25 12:59:42 (Show Source): You can put this solution on YOUR website!1. (A v B) → (C • D) / A → C ---------------------------- 2. A Assumption 3. C • D 1,2 Modus Ponens 4. C 3 Simplification 5. A -> C 2,4 Conditional Proof