SOLUTION: x^4-20x^3+96x^2 could you help me solve this problem on factoring trinomials.

Question 171902This question is from textbook
: x^4-20x^3+96x^2 could you help me solve this problem on factoring trinomials. This question is from textbook

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 96 respectively.

Now multiply the first coefficient 1 and the last coefficient 96 to get 96. Now what two numbers multiply to 96 and add to the middle coefficient -20? Let's list all of the factors of 96:

Factors of 96:
1,2,3,4,6,8,12,16,24,32,48,96

-1,-2,-3,-4,-6,-8,-12,-16,-24,-32,-48,-96 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 96
1*96
2*48
3*32
4*24
6*16
8*12
(-1)*(-96)
(-2)*(-48)
(-3)*(-32)
(-4)*(-24)
(-6)*(-16)
(-8)*(-12)

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

Now which of these pairs add to -20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -20

First Number	Second Number	Sum
1	96	1+96=97
2	48	2+48=50
3	32	3+32=35
4	24	4+24=28
6	16	6+16=22
8	12	8+12=20
-1	-96	-1+(-96)=-97
-2	-48	-2+(-48)=-50
-3	-32	-3+(-32)=-35
-4	-24	-4+(-24)=-28
-6	-16	-6+(-16)=-22
-8	-12	-8+(-12)=-20

From this list we can see that -8 and -12 add up to -20 and multiply to 96

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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