SOLUTION: I need your help in Factoring this problem. It must be factored completely. x^5y^3 - 9x^4y^2 + 20x^3y I have tried, but I am coming up with an incorrect answer. My answer:

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need your help in Factoring this problem. It must be factored completely. x^5y^3 - 9x^4y^2 + 20x^3y I have tried, but I am coming up with an incorrect answer. My answer:      Log On


   

Question 143604: I need your help in Factoring this problem. It must be factored completely.
x^5y^3 - 9x^4y^2 + 20x^3y
I have tried, but I am coming up with an incorrect answer.
My answer: x^3y(x -x5)(x - 4)
= x^3y [(x0(x) - (x)(-4) - (-5)(x) + (-5)(-4)]
= x^3y(x^2) - (4x^2) - (5x^2) + 20
= x^5y - 9x^2 + 20
I am unsure of how to determine the Greatest common factor on this type of problem.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E5y%5E3-9x%5E4y%5E2%2B20x%5E3y Start with the given expression


x%5E3y%28x%5E2y%5E2-9xy%2B20%29 Factor out the GCF x%5E3y


Now let's focus on the inner expression x%5E2y%5E2-9xy%2B20




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Looking at 1x%5E2y%5E2-9xy%2B20 we can see that the first term is 1x%5E2y%5E2 and the last term is 20 where the coefficients are 1 and 20 respectively.

Now multiply the first coefficient 1 and the last coefficient 20 to get 20. Now what two numbers multiply to 20 and add to the middle coefficient -9? Let's list all of the factors of 20:



Factors of 20:
1,2,4,5,10,20

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

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

note: remember two negative numbers multiplied together make a positive 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
1201+20=21
2102+10=12
454+5=9
-1-20-1+(-20)=-21
-2-10-2+(-10)=-12
-4-5-4+(-5)=-9



From this list we can see that -4 and -5 add up to -9 and multiply to 20


Now looking at the expression 1x%5E2y%5E2-9xy%2B20, replace -9xy with -4xy%2B-5xy (notice -4xy%2B-5xy adds up to -9xy. So it is equivalent to -9xy)

1x%5E2y%5E2%2Bhighlight%28-4xy%2B-5xy%29%2B20


Now let's factor 1x%5E2y%5E2-4xy-5xy%2B20 by grouping:


%281x%5E2y%5E2-4xy%29%2B%28-5xy%2B20%29 Group like terms


xy%28xy-4%29-5%28xy-4%29 Factor out the GCF of xy out of the first group. Factor out the GCF of -5 out of the second group


%28xy-5%29%28xy-4%29 Since we have a common term of xy-4, we can combine like terms

So 1x%5E2y%5E2-4xy-5xy%2B20 factors to %28xy-5%29%28xy-4%29


So this also means that 1x%5E2y%5E2-9xy%2B20 factors to %28xy-5%29%28xy-4%29 (since 1x%5E2y%5E2-9xy%2B20 is equivalent to 1x%5E2y%5E2-4xy-5xy%2B20)



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So our expression goes from x%5E3y%28x%5E2y%5E2-9xy%2B20%29 and factors further to x%5E3y%28xy-5%29%28xy-4%29


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Answer:

So x%5E5y%5E3-9x%5E4y%5E2%2B20x%5E3y factors to x%5E3y%28xy-5%29%28xy-4%29