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test/140011: Factor completely and match your result to the correct answer below.
r2 + 2r – 80
A)(r + 10)(r + 8)
B)(r – 10)(r + 8)
C)(r – 10)(r – 8)
D)(r + 10)(r – 8)

1 solutions

Answer 102038 by jim_thompson5910(28595)   on 2008-05-04 19:30:54 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -80 respectively.

Now multiply the first coefficient 1 and the last coefficient -80 to get -80. Now what two numbers multiply to -80 and add to the middle coefficient 2? Let's list all of the factors of -80:

Factors of -80:
1,2,4,5,8,10,16,20,40,80

-1,-2,-4,-5,-8,-10,-16,-20,-40,-80 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -80
(1)*(-80)
(2)*(-40)
(4)*(-20)
(5)*(-16)
(8)*(-10)
(-1)*(80)
(-2)*(40)
(-4)*(20)
(-5)*(16)
(-8)*(10)

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

Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2

First NumberSecond NumberSum
1-801+(-80)=-79
2-402+(-40)=-38
4-204+(-20)=-16
5-165+(-16)=-11
8-108+(-10)=-2
-180-1+80=79
-240-2+40=38
-420-4+20=16
-516-5+16=11
-810-8+10=2

From this list we can see that -8 and 10 add up to 2 and multiply to -80

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 factors to

 test/140010: Factor: st + 5b – bs – 5t A) (s – 5)(t + b) B) (s – 5)(t – b) C) (s + 5)(t – b) D) The expression is prime. 1 solutions Answer 102037 by jim_thompson5910(28595)   on 2008-05-04 19:29:15 (Show Source): You can put this solution on YOUR website! Start with the given expression Rearrange the terms Group like terms Factor out the GCF "s" from the first group. Factor out the GCF -5 from the second group Rearrange in the second group to get Combine like terms ----------------------------- Answer: So factors to
 test/140008: Factor completely: 12p2 + 20p A)2(6p2 + 10) B)4p(3p + 20) C)4p(3p + 5) D)6p(2p + 5) 1 solutions Answer 102036 by jim_thompson5910(28595)   on 2008-05-04 19:23:36 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF ----------------------------------------------------------- Answer: So factors to
test/140007: Factor: z2 – 14z + 49
A) (z – 7)2
B) (z – 7)(z + 7)
C) (z – 14)(z + 1)
D) The expression is prime.

1 solutions

Answer 102035 by jim_thompson5910(28595)   on 2008-05-04 19:21:53 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 49 respectively.

Now multiply the first coefficient 1 and the last coefficient 49 to get 49. Now what two numbers multiply to 49 and add to the middle coefficient -14? Let's list all of the factors of 49:

Factors of 49:
1,7

-1,-7 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 49
1*49
7*7
(-1)*(-49)
(-7)*(-7)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14

First NumberSecond NumberSum
1491+49=50
777+7=14
-1-49-1+(-49)=-50
-7-7-7+(-7)=-14

From this list we can see that -7 and -7 add up to -14 and multiply to 49

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 )

note: is equivalent to since the term occurs twice. So also factors to

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

So factors to

 test/140006: Factor: y2 – 64 A) (y – 8)(y + 8) B) (y – 8)2 C) (8 – y)(8 + y) D) The expression is prime. 1 solutions Answer 102034 by jim_thompson5910(28595)   on 2008-05-04 19:21:05 (Show Source): You can put this solution on YOUR website! Start with the given expression Rewrite as Rewrite as Now use the difference of squares. Remember, the difference of squares formula is where in this case and Plug in and So the expression factors to Notice that if you foil the factored expression, you get the original expression. This verifies our answer.
 Geometric_formulas/139954: 1 solutions Answer 102009 by jim_thompson5910(28595)   on 2008-05-04 13:25:13 (Show Source): You can put this solution on YOUR website!Let x=supplement to angle A Remember, supplement angles add to 180. So if we want to find the supplement to angle A, then Subtract 72 from both sides Combine like terms on the right side -------------------------------------------------------------- Answer: So our answer is So the supplement to angle A is 108 degrees
 Geometric_formulas/139952: 7. Find the measure of angle x and measure of angle y. 1 solutions Answer 102008 by jim_thompson5910(28595)   on 2008-05-04 13:20:11 (Show Source): You can put this solution on YOUR website!Notice how angle x and 135 degrees form a 180 degree angle. So this means that Subtract 135 from both sides Combine like terms on the right side Also, notice how angle x and angle y also form a 180 degree angle. So But we know what x is, so plug in the value of x Plug in Subtract 45 from both sides Combine like terms on the right side -------------------------------------------------------------- Answer: So the values are and
 Geometric_formulas/139951: 6. Find the missing angle. 1 solutions Answer 102006 by jim_thompson5910(28595)   on 2008-05-04 13:14:15 (Show Source): You can put this solution on YOUR website!To find the missing angle, first add up the two given angles So the sum of the two angles is 148 degrees. Now subtract this answer from 180 (remember the sum of the three angles of a triangle is 180 degrees) So the missing angle is 32 degrees
 Geometric_formulas/139950: 5. Which two triangles are similar? 1 solutions Answer 102005 by jim_thompson5910(28595)   on 2008-05-04 13:08:48 (Show Source): You can put this solution on YOUR website!First, we need to find the missing angles of each triangle. For the first triangle, first add up the two given angles 69 and 48 to get Now subtract 117 from 180 to get So the first triangle has these angles --------------------------------------------------------- For the second triangle, first add up the two given angles 63 and 48 to get Now subtract 111 from 180 to get So the second triangle has these angles ------------------------------------------------------------ For the third triangle, first add up the two given angles 63 and 48 to get Now subtract 111 from 180 to get So the third triangle has these angles ---------------------------------------------------------- Summary: So the three triangles have these angles ---------------------------------------------------------- Answer: Remember, similar triangles have equal angles. From the figure, we can see that triangles a) and b) have equal angles. So triangles a) and b) are similar triangles.
 Geometric_formulas/139948: 4. The two triangles are similar. Find the indicated side. Find y. 1 solutions Answer 102003 by jim_thompson5910(28595)   on 2008-05-04 12:54:18 (Show Source): You can put this solution on YOUR website!Since the triangles are similar, this means that the length of the sides are dependent on one another. In fact, these sides form the ratio: Multiply both sides by y Multiply both sides by 8 Multiply Divide both sides by 10 Simplify So our answer is
 Geometric_formulas/139946: 3. Identify the hypotenuse of the triangle by giving its letter 1 solutions Answer 102002 by jim_thompson5910(28595)   on 2008-05-04 12:48:23 (Show Source): You can put this solution on YOUR website!The hypotenuse is the longest side. So in this case, the hypotenuse is z.
 Geometric_formulas/139945: Find the missing length of the right triangle 1 solutions Answer 102001 by jim_thompson5910(28595)   on 2008-05-04 12:45:30 (Show Source): You can put this solution on YOUR website! Let's use Pythagoreans theorem to solve this problem Pythagoreans theorem: where a and b are the legs of the triangle and c is the hypotenuse Plug in a=7, b=24. Now lets solve for c. Square each individual term Combine like terms Take the square root of both sides Simplify the square root So our answer is So the length of the unknown side is 25 units.
 Geometric_formulas/139941: 1. Approximate by giving the two whole numbers that it lies between1 solutions Answer 102000 by jim_thompson5910(28595)   on 2008-05-04 12:10:17 (Show Source): You can put this solution on YOUR website!First, note that the numbers 25 and 36 are perfect squares. In other words, and . So since 31 is in between 25 and 36, this means that the square root of 31 is in between 5 and 6. In other words, since , this means . Notice how 31 is 6 units away from 25 and 5 units away from 36. So 31 is about the halfway point from 25 to 36. So a good approximation for is 5.5 since 5.5 is halfway between 5 and 6. So If we take the square root of 31 with a calculator, we get . So this shows us that our approximation is very close.
 Equations/139872: Find the slope of a line whose equation is y= -6x+31 solutions Answer 101938 by jim_thompson5910(28595)   on 2008-05-03 15:09:29 (Show Source): You can put this solution on YOUR website!Notice how is in slope-intercept form where m is the slope and b is the y-intercept. So this shows us that the slope is and the y-intercept is
 Quadratic_Equations/139853: Please help me solve this equation: 5x+4y=12 I have tried the equation by doing this: 5x+4y=12 5x-5x+4y=12-5x 4y=12-5x 4y/4=12-5x/4 My answer came totaled to: y=3-5x1 solutions Answer 101934 by jim_thompson5910(28595)   on 2008-05-03 14:14:02 (Show Source): You can put this solution on YOUR website!Do you want to solve for y? Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce
 Polynomials-and-rational-expressions/139800: Solve for z: z^2-2z+1=-41 solutions Answer 101926 by jim_thompson5910(28595)   on 2008-05-03 11:25:36 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 4 to both sides. Combine like terms Let's use the quadratic formula to solve for z: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=-2, and c=5 Negate -2 to get 2 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .) Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 1 to get 2 After simplifying, the quadratic has roots of or
 Complex_Numbers/139806: please help solve Divide and express the result in standard form 6 -5i / 8 + 4i1 solutions Answer 101925 by jim_thompson5910(28595)   on 2008-05-03 11:22:33 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply the fraction by Foil and Multiply Break up the fraction. Reduce. So the expression is now in form where and
Polynomials-and-rational-expressions/139640: Hi, I am having trouble with a problem I hope some one can help me please.
Factor Completety:
3x - 3x^2 + 6x - 18
I would like to thank you for your help.
1 solutions

Answer 101798 by jim_thompson5910(28595)   on 2008-05-01 20:48:46 (Show Source):
You can put this solution on YOUR website!
Are you sure it's not supposed to read: ???

Combine like terms

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 1 and -6 respectively.

Now multiply the first coefficient 1 and the last coefficient -6 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient 1? Let's list all of the factors of -6:

Factors of -6:
1,2,3,6

-1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -6
(1)*(-6)
(2)*(-3)
(-1)*(6)
(-2)*(3)

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

Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

First NumberSecond NumberSum
1-61+(-6)=-5
2-32+(-3)=-1
-16-1+6=5
-23-2+3=1

From this list we can see that -2 and 3 add up to 1 and multiply to -6

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 factors to

 test/139597: This question is from textbook factoring using the Distributive property. x3+3x2-4x-121 solutions Answer 101786 by jim_thompson5910(28595)   on 2008-05-01 18:40:13 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms Factor by using the difference of squares to get So factors to
 Exponential-and-logarithmic-functions/139562: This question is from textbook College Algrbra Find (f o g)(16) if f(x)=3^x and f(x)=log4(x) I got this far g(16)=log4(16)=4 Please help.Thanks1 solutions Answer 101784 by jim_thompson5910(28595)   on 2008-05-01 18:29:09 (Show Source): You can put this solution on YOUR website!Remember (f o g)(x) is the same as f(g(x)) So (f o g)(16)=f(g(16)) So (note: asks: "4 raised to what power gives me 16?". Since , this means ) So g(16)=2 Now this means that f(g(16))=f(2) So f(g(16))=9
Quadratic_Equations/139592: This question is from textbook
Factor each expression.
x2-3x-40
1 solutions

Answer 101783 by jim_thompson5910(28595)   on 2008-05-01 18:23:39 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -40 respectively.

Now multiply the first coefficient 1 and the last coefficient -40 to get -40. Now what two numbers multiply to -40 and add to the middle coefficient -3? Let's list all of the factors of -40:

Factors of -40:
1,2,4,5,8,10,20,40

-1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -40
(1)*(-40)
(2)*(-20)
(4)*(-10)
(5)*(-8)
(-1)*(40)
(-2)*(20)
(-4)*(10)
(-5)*(8)

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

Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3

First NumberSecond NumberSum
1-401+(-40)=-39
2-202+(-20)=-18
4-104+(-10)=-6
5-85+(-8)=-3
-140-1+40=39
-220-2+20=18
-410-4+10=6
-58-5+8=3

From this list we can see that 5 and -8 add up to -3 and multiply to -40

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 factors to

expressions/139593: This question is from textbook
Factor each expression.
5x2+16x+3
1 solutions

Answer 101782 by jim_thompson5910(28595)   on 2008-05-01 18:21:36 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 5 and 3 respectively.

Now multiply the first coefficient 5 and the last coefficient 3 to get 15. Now what two numbers multiply to 15 and add to the middle coefficient 16? Let's list all of the factors of 15:

Factors of 15:
1,3,5,15

-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 15
1*15
3*5
(-1)*(-15)
(-3)*(-5)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 16

First NumberSecond NumberSum
1151+15=16
353+5=8
-1-15-1+(-15)=-16
-3-5-3+(-5)=-8

From this list we can see that 1 and 15 add up to 16 and multiply to 15

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 factors to

Miscellaneous_Word_Problems/139591: This question is from textbook Algebra Structure and Method
I have been struggling with this problem and I was wondering if anyone could help me? I would deeply appreciate it! Please and Thank you!

Factoring Patterns for ax^2+bx+c
Factor. Check by multiplying the factors. If the polynomial is not factorable, write prime.
2(x-y)^2-9(x-y)z-5z^2
1 solutions

Answer 101781 by jim_thompson5910(28595)   on 2008-05-01 18:19:59 (Show Source):
You can put this solution on YOUR website!

Let

Plug in

Sort the terms in descending order

Factor out a negative one

Now let's factor the inner polynomial

Looking at we can see that the first term is and the last term is where the coefficients are 5 and -2 respectively.

Now multiply the first coefficient 5 and the last coefficient -2 to get -10. Now what two numbers multiply to -10 and add to the middle coefficient 9? Let's list all of the factors of -10:

Factors of -10:
1,2,5,10

-1,-2,-5,-10 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -10
(1)*(-10)
(2)*(-5)
(-1)*(10)
(-2)*(5)

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

Now which of these pairs add to 9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 9

First NumberSecond NumberSum
1-101+(-10)=-9
2-52+(-5)=-3
-110-1+10=9
-25-2+5=3

From this list we can see that -1 and 10 add up to 9 and multiply to -10

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 factors to

This means that factors to (remember, we pulled out a negative one previously)

Now replace "w" with

Distribute

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

So factors to

 Radicals/139576: If √96 is simplified to a√b such that a and b are integers, what is the value of a? √ = Radical sign Thank you, in advance.1 solutions Answer 101780 by jim_thompson5910(28595)   on 2008-05-01 18:12:17 (Show Source): You can put this solution on YOUR website! Start with the given expression The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number. So let's list the factors of 96 Factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 Notice how 16 is the largest perfect square, so lets factor 96 into 16*6 Factor 96 into 16*6 Break up the square roots using the identity Take the square root of the perfect square 16 to get 4 So the expression simplifies to ----------------------------------------------------- Answer: So in this case, the value of ---------------------------- Check: Notice if we evaluate the square root of 96 with a calculator we get and if we evaluate we get This shows that . So this verifies our answer
Miscellaneous_Word_Problems/139589: This question is from textbook Algebra Structure and Method
I have been struggling with this problem for awhile now and I was wondering if anyone could help me? I would deeply appreciate it! Please and Thank you!

Factoring Patterns for ax^2+bx+c
Factor. Check by multiplying the factors. If the polynomial is not factorable, write prime.
8+45r-18r^2
1 solutions

Answer 101779 by jim_thompson5910(28595)   on 2008-05-01 18:09:59 (Show Source):
You can put this solution on YOUR website!

Sort the terms in descending order

Factor out a negative one

Looking at the inner polynomial , we can see that the first term is and the last term is -8

Now multiply the first coefficient 18 and the last term -8 to get -144. Now what two numbers multiply to -144 and add to the middle coefficient -45? Let's list all of the factors of -144:

Factors of -144:
1,2,3,4,6,8,9,12,16,18,24,36,48,72

-1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -144
(1)*(-144)
(2)*(-72)
(3)*(-48)
(4)*(-36)
(6)*(-24)
(8)*(-18)
(9)*(-16)
(-1)*(144)
(-2)*(72)
(-3)*(48)
(-4)*(36)
(-6)*(24)
(-8)*(18)
(-9)*(16)

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

Now which of these pairs add to -45? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -45

First NumberSecond NumberSum
1-1441+(-144)=-143
2-722+(-72)=-70
3-483+(-48)=-45
4-364+(-36)=-32
6-246+(-24)=-18
8-188+(-18)=-10
9-169+(-16)=-7
-1144-1+144=143
-272-2+72=70
-348-3+48=45
-436-4+36=32
-624-6+24=18
-818-8+18=10
-916-9+16=7

From this list we can see that 3 and -48 add up to -45 and multiply to -144

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 factors to

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