# SOLUTION: Factor completely 8x^2 -32x +24

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Question 88151: Factor completely
8x^2 -32x +24

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Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)
In order to factor , first multiply the leading coefficient 8 and the last term 24 to get 192. Now we need to ask ourselves: What two numbers multiply to 192 and add to -32? Lets find out by listing all of the possible factors of 192

Factors:

1,2,3,4,6,8,12,16,24,32,48,64,96,192,

-1,-2,-3,-4,-6,-8,-12,-16,-24,-32,-48,-64,-96,-192, List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to 192.

1*192=192

2*96=192

3*64=192

4*48=192

6*32=192

8*24=192

12*16=192

(-1)*(-192)=192

(-2)*(-96)=192

(-3)*(-64)=192

(-4)*(-48)=192

(-6)*(-32)=192

(-8)*(-24)=192

(-12)*(-16)=192

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

Now which of these pairs add to -32? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -32

||||||||||||||
 First Number | Second Number | Sum 1 | 192 | 1+192=193 2 | 96 | 2+96=98 3 | 64 | 3+64=67 4 | 48 | 4+48=52 6 | 32 | 6+32=38 8 | 24 | 8+24=32 12 | 16 | 12+16=28 -1 | -192 | -1+(-192)=-193 -2 | -96 | -2+(-96)=-98 -3 | -64 | -3+(-64)=-67 -4 | -48 | -4+(-48)=-52 -6 | -32 | -6+(-32)=-38 -8 | -24 | -8+(-24)=-32 -12 | -16 | -12+(-16)=-28

We can see from the table that -8 and -24 add to -32. So the two numbers that multiply to 192 and add to -32 are: -8 and -24

breaks down to this (just replace with the two numbers that multiply to 192 and add to -32, which are: -8 and -24)

Replace with

Group the first two terms together and the last two terms together like this:

Factor a 8 out of the first group and factor a -24 out of the second group.

Now since we have a common term we can combine the two terms.

Combine like terms.
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