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test/375129: 10x³-51x²+54x
1 solutions

Answer 266756 by jim_thompson5910(28598)   on 2010-11-22 18:37:28 (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor.

Factor out the GCF .

Now let's try to factor the inner expression

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

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 :
1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
-1,-2,-3,-4,-5,-6,-9,-10,-12,-15,-18,-20,-27,-30,-36,-45,-54,-60,-90,-108,-135,-180,-270,-540

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

These factors pair up and multiply to .
1*540 = 540
2*270 = 540
3*180 = 540
4*135 = 540
5*108 = 540
6*90 = 540
9*60 = 540
10*54 = 540
12*45 = 540
15*36 = 540
18*30 = 540
20*27 = 540
(-1)*(-540) = 540
(-2)*(-270) = 540
(-3)*(-180) = 540
(-4)*(-135) = 540
(-5)*(-108) = 540
(-6)*(-90) = 540
(-9)*(-60) = 540
(-10)*(-54) = 540
(-12)*(-45) = 540
(-15)*(-36) = 540
(-18)*(-30) = 540
(-20)*(-27) = 540

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

First NumberSecond NumberSum
15401+540=541
22702+270=272
31803+180=183
41354+135=139
51085+108=113
6906+90=96
9609+60=69
105410+54=64
124512+45=57
153615+36=51
183018+30=48
202720+27=47
-1-540-1+(-540)=-541
-2-270-2+(-270)=-272
-3-180-3+(-180)=-183
-4-135-4+(-135)=-139
-5-108-5+(-108)=-113
-6-90-6+(-90)=-96
-9-60-9+(-60)=-69
-10-54-10+(-54)=-64
-12-45-12+(-45)=-57
-15-36-15+(-36)=-51
-18-30-18+(-30)=-48
-20-27-20+(-27)=-47

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 then factors further to

===============================================================

So completely factors to .

In other words, .

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

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

 Reduction-of-unit-multipliers/375128: find the measures of the side of a square with an area of 75 sq. units 1 solutions Answer 266755 by jim_thompson5910(28598)   on 2010-11-22 18:36:12 (Show Source): You can put this solution on YOUR website! Start with the area of a square formula. Take the square root of both sides (note: we're only taking the positive square root since a negative length doesn't make sense). Flip the equation. Plug in . Simplify the square root. Evaluate the right side with a calculator. So if a square has an area of square units, then it has a side length of approximately units.
 Polynomials-and-rational-expressions/375099: (s+1/5)(s+1/5) Please help me simplify?1 solutions Answer 266753 by jim_thompson5910(28598)   on 2010-11-22 18:33:55 (Show Source): You can put this solution on YOUR website! Start with the given expression. Now let's FOIL the expression. Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms:. Multiply the Outer terms:. Multiply the Inner terms:. Multiply the Last terms:. --------------------------------------------------- So we have the terms: , , , Now add every term listed above to make a single expression. Now combine like terms. So FOILs to . In other words, . If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Polynomials-and-rational-expressions/375125: (x^2 - 7) + ( x^2 + 7) 1 solutions Answer 266752 by jim_thompson5910(28598)   on 2010-11-22 18:28:41 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Polynomials-and-rational-expressions/375104: The problem asks me to simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. √(32a^2 b)1 solutions Answer 266750 by jim_thompson5910(28598)   on 2010-11-22 18:27:50 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor into Break up the square root using the identity . Take the square root of to get . Take the square root of to get . Recombine the roots and rearrange the terms. ================================================== Answer: So simplifies to In other words, where every variable is non-negative. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Inequalities/375112: how do I solve 8-6x<8x-4x1 solutions Answer 266748 by jim_thompson5910(28598)   on 2010-11-22 18:25:53 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Combine like terms on the right side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Inequalities/375114: how do I solve 2x+9>6x+111 solutions Answer 266747 by jim_thompson5910(28598)   on 2010-11-22 18:25:17 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from 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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Radicals/375116: Write each expression below in simplest radical form. SHOW YOUR STEPS. √4x^8 I'm pretty sure that the answer is 2x^4√, but how do I show the steps? I'd appreciate some help! Thank you! :)1 solutions Answer 266746 by jim_thompson5910(28598)   on 2010-11-22 18:24:26 (Show Source): You can put this solution on YOUR website! Start with the given expression. 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 multiply the terms. ================================================== Answer: So simplifies to In other words, where x is nonnegative. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Polynomials-and-rational-expressions/375091: Please help me simplify by removing factors of 1. (p^2-9)/〖(p+3)〗^2 1 solutions Answer 266744 by jim_thompson5910(28598)   on 2010-11-22 18:21:23 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Graphs/375069: How do I solve this equation? graphing this equation y = -3/4x-3. Been working on it but can't figure it out,I think the y intercept is -31 solutions Answer 266729 by jim_thompson5910(28598)   on 2010-11-22 17:13:33 (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 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 -3 and the run is 4. This means that to go from point to point, we can go down 3 and over 4 So starting at , go down 3 units and to the right 4 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 If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Quadratic_Equations/375065: Hello everyone, finding the following question puzzling, i have not covered this before, and am trying to get a heads up for when i start my course Use logarithmic differentiation to differentiate the following: (i) y = 2^x (ii) y = x^x Cheers1 solutions Answer 266728 by jim_thompson5910(28598)   on 2010-11-22 17:12:31 (Show Source): You can put this solution on YOUR website!i) Start with the given equation. Take the natural log of both sides. Pull down the exponent. ... Derive both sides ... Solve for y' ... Now plug in Note: the derivative of is ----------------------------------------------- ii) Start with the given equation. Take the natural log of both sides. Pull down the exponent. ... Derive both sides ... Solve for y' ... Now plug in
 expressions/375057: 12-3n+4(2n+5)1 solutions Answer 266727 by jim_thompson5910(28598)   on 2010-11-22 17:06:32 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Exponents/375058: Please help simplify the following: 36r/6r^2s1 solutions Answer 266725 by jim_thompson5910(28598)   on 2010-11-22 17:04:21 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Expressions-with-variables/375061: Trying to help my daughter, can you solve for X x(1+4)=z Thanks, Jon1 solutions Answer 266724 by jim_thompson5910(28598)   on 2010-11-22 17:02:31 (Show Source): You can put this solution on YOUR website! Start with the given equation. Divide both sides by . Add So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Linear-equations/375059: find an equation that satisfies the points (9,136) and (3,40)1 solutions Answer 266722 by jim_thompson5910(28598)   on 2010-11-22 17:01:20 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Distribute Multiply Add 136 to both sides. Combine like terms. Simplify So the equation that goes through the points and is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Linear-systems/375053: what formula you use to find out the area of a triangel1 solutions Answer 266719 by jim_thompson5910(28598)   on 2010-11-22 16:49:00 (Show Source): You can put this solution on YOUR website!Area of a triangle = (base*height)/2
 Parallelograms/375051: Okay In Finding The Area Of Parellogram what do you do???1 solutions Answer 266718 by jim_thompson5910(28598)   on 2010-11-22 16:46:27 (Show Source): You can put this solution on YOUR website!Area of parallelogram = Base * height
 Radicals/375049: Divide and simplify so that there are no radicals in the denominator. SHOW YOUR STEPS. √ 7/100 I didn't really know how to type it out, but the --> √ <-- thing is supposed to be for both the 7 and the ten. I have no clue how to solve this problem, can someone please help me? Thanks so much! I'd really appreciate it :)1 solutions Answer 266717 by jim_thompson5910(28598)   on 2010-11-22 16:45:36 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Radicals/375045: Divide and simplify so that there are no radicals in the denominator. SHOW YOUR STEPS. √18+√24/√6 I don't know how to do this kind of problem at all, can someone help me, please? Thanks so much! :)1 solutions Answer 266716 by jim_thompson5910(28598)   on 2010-11-22 16:44:08 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor 18 into 3*6 and factor 24 into 4*6 (notice the presence of 6) Break up the square roots using the identity Take the square root of 4 to get 2. Factor out the GCF Highlight the common terms. Cancel out the common terms. Simplify. So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Radicals/375044: Divide and simplify so that there are no radicals in the denominator. SHOW YOUR STEPS. 8/6√ PLEEEEASE help me!!!!!!! I'd really appreciate some help because I am totally stuck on this. Thank you!!!!! :)1 solutions Answer 266715 by jim_thompson5910(28598)   on 2010-11-22 16:35:10 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Polynomials-and-rational-expressions/374979: I am having an issue solving a subtraction problem. Could you please help. The problem is as follows: (-2a+3b-c)-(-7b+3c-3d) Please help!!!1 solutions Answer 266714 by jim_thompson5910(28598)   on 2010-11-22 16:32:50 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Age_Word_Problems/375011: Bill is 6 years older than Tom. Three years ago, Bill's age was four times Tom's age. What are the boys ages now? How do I write this in a single variable equation? I have tried and I have gotten this wrong on two different quizzes, so I am curious what the correct answer is?1 solutions Answer 266713 by jim_thompson5910(28598)   on 2010-11-22 16:30:02 (Show Source): You can put this solution on YOUR website!Let B = bill's age now, T = Tom's age now So Bill's age 3 yrs ago was and Tom's age 3 yrs ago was Since "Bill is 6 years older than Tom", we know that Also, because "Bill's age was four times Tom's age", we know that ------------------------- Start with the second equation. Plug in (ie replace each 'B' with 'T+6'). So this would be the starting point of the single variable equation you're looking for. Distribute. Combine like terms on the left side. Subtract from 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 . Reduce. So this means that Tom is 5 yrs old. Now plug this value into to get . So which means that Bill is 11 yrs old. Notice that 3 yrs ago, Bill was 11-3=8 yrs old and Tom was 5-3=2 years old. Also notice that 8 is 4 times 2. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Numeric_Fractions/375031: 13y/16 divided by 5/131 solutions Answer 266712 by jim_thompson5910(28598)   on 2010-11-22 16:23:11 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
Quadratic_Equations/375035: What 2 numbers have a product of 128 and a sum of 48?
I don't believe it has a solution with whole numbers anyway.

1 solutions

Answer 266710 by jim_thompson5910(28598)   on 2010-11-22 16:21:14 (Show Source):
You can put this solution on YOUR website!
To find these two numbers, we need to list all of the factors of .

Factors of :
1,2,4,8,16,32,64,128
-1,-2,-4,-8,-16,-32,-64,-128

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

These factors pair up and multiply to .
1*128 = 128
2*64 = 128
4*32 = 128
8*16 = 128
(-1)*(-128) = 128
(-2)*(-64) = 128
(-4)*(-32) = 128
(-8)*(-16) = 128

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

First NumberSecond NumberSum
11281+128=129
2642+64=66
4324+32=36
8168+16=24
-1-128-1+(-128)=-129
-2-64-2+(-64)=-66
-4-32-4+(-32)=-36
-8-16-8+(-16)=-24

From the table, we can see that there are no pairs of numbers which add to .

So you are correct. There are no two rational numbers which multiply to 128 and add to 48.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

 Linear-systems/375032: y=3x 2x+y=5 This is the substitution method.its one problem.Please help me find the answer to this problem1 solutions Answer 266709 by jim_thompson5910(28598)   on 2010-11-22 16:16:59 (Show Source): You can put this solution on YOUR website! Start with the second equation. Plug in (ie replace every 'y' with '3x') Combine like terms on the left side. Divide both sides by to isolate . Reduce. Go back to the first equation. Plug in Multiply So the answers are and which form the ordered pair (1,3) This means that the system is consistent and independent. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 logarithm/374721: Hello, Could you please assist me with solving the following equation for x: log x = -1/6 64 Thank You1 solutions Answer 266520 by jim_thompson5910(28598)   on 2010-11-22 00:19:51 (Show Source): You can put this solution on YOUR website!Remember that we can rewrite as So this means that we can rewrite as Start with the given equation. Rewrite as Use the identity Multiply Reduce. Flip the base to make the exponent positive. Evaluate to get 2. So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Quadratic-relations-and-conic-sections/374779: what is the equation of the circle that has its center at (3,-1) and passes through the point (-2,2)1 solutions Answer 266518 by jim_thompson5910(28598)   on 2010-11-22 00:12:32 (Show Source): You can put this solution on YOUR website! Start with the general equation of a circle. Plug in and (since the center is the point (h,k) ). Plug in and (this is the point that lies on the circle, which is in the form (x,y) ). Combine like terms. Square each term. Add. So because , , and , this means that the equation of the circle with center (3,-1) that goes through the point (-2,2) is . If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Quadratic-relations-and-conic-sections/374780: The two points (-2,4) and (4,2) are the endpoints of the diameter of a circle. What is the equation of this circle in standard form?1 solutions Answer 266517 by jim_thompson5910(28598)   on 2010-11-22 00:10:35 (Show Source): You can put this solution on YOUR website!Recall that the general equation of a circle is . So we need the center (h,k) and the radius squared . First, let's find the center (h,k). Since the center is the midpoint of the line segment with endpoints (-2,4) and (4,2), we need to find the midpoint. X-Coordinate of Midpoint = Since the x coordinate of midpoint is , this means that Y-Coordinate of Midpoint = Since the y coordinate of midpoint is , this means that So the center is the point (1, 3) --------------------------------------------------- Now let's find the radius squared Use the formula , where (h,k) is the center and (x,y) is an arbitrary point on the circle. In this case, and . Also, and . Plug these values into the equation above and simplify to get: So because , , and , this means that the equation of the circle that passes through the points (-2,4) and (4,2) (which are the endpoints of the diameter) is . If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Polynomials-and-rational-expressions/374775: Solve for x: x/8-x/12=1/8 Please help. Thank you.1 solutions Answer 266516 by jim_thompson5910(28598)   on 2010-11-22 00:08:25 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply EVERY term by the LCD to clear out all of the fractions. Multiply and simplify. Combine like terms on the left side. ---------------------------------------------------------------------- Answer: So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Parallelograms/374778: i forgot my geometry book at my school. can anyone tell me the problem 12-18 evens for 5.6?1 solutions Answer 266513 by jim_thompson5910(28598)   on 2010-11-22 00:02:07 (Show Source): You can put this solution on YOUR website!Sorry, we don't have your book either.