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

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

Looking at the expression x%5E2-8x-32, we can see that the first coefficient is 1, the second coefficient is -8, and the last term is -32.


Now multiply the first coefficient 1 by the last term -32 to get %281%29%28-32%29=-32.


Now the question is: what two whole numbers multiply to -32 (the previous product) and add to the second coefficient -8?


To find these two numbers, we need to list all of the factors of -32 (the previous product).


Factors of -32:
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 -32.
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 -8:


First NumberSecond NumberSum
1-321+(-32)=-31
2-162+(-16)=-14
4-84+(-8)=-4
-132-1+32=31
-216-2+16=14
-48-4+8=4



From the table, we can see that there are no pairs of numbers which add to -8.

So x%5E2-8x-32 cannot be factored. Make sure that you have the correct problem written down.