SOLUTION: Factor completely x^10y^3 � 4x^9y^2 � 21x^8y

Question 146160: Factor completely

x^10y^3 � 4x^9y^2 � 21x^8y

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

Factor out the GCF

Now let's focus on the inner expression

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Looking at we can see that the first term is and the last term is where the coefficients are 1 and -21 respectively.

Now multiply the first coefficient 1 and the last coefficient -21 to get -21. Now what two numbers multiply to -21 and add to the middle coefficient -4? Let's list all of the factors of -21:

Factors of -21:
1,3,7,21

-1,-3,-7,-21 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -21
(1)*(-21)
(3)*(-7)
(-1)*(21)
(-3)*(7)

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

Now which of these pairs add to -4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -4

First Number	Second Number	Sum
1	-21	1+(-21)=-20
3	-7	3+(-7)=-4
-1	21	-1+21=20
-3	7	-3+7=4

From this list we can see that 3 and -7 add up to -4 and multiply to -21

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 )

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So our expression goes from and factors further to

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Answer:

So factors to

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