SOLUTION: how do you factor x squared minus eight x minus 32?

Question 192174: how do you factor x squared minus eight x minus 32?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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 :
1,2,4,8,16,32
-1,-2,-4,-8,-16,-32

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

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

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

First Number	Second Number	Sum
1	-32	1+(-32)=-31
2	-16	2+(-16)=-14
4	-8	4+(-8)=-4
-1	32	-1+32=31
-2	16	-2+16=14
-4	8	-4+8=4

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

So cannot be factored. Make sure that you have the correct problem written down.

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