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Find all integers for "a" in which x^2+ax-32 can be factored

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2 Answers

-32 = -1*32 = -32*1 = -2*16 = -16*2 = -4*8 = -8*4
So, a = 31, -31, 14, -14, 4, -4
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Attn: a = sum of any pair of factors of -32.
Hi Ryan;
x2+ax-32
I believe the question is all integers which can be inserted for a in the following FOIL...
(x+??)[x+(-?)] or [x+(-??)](x+?)
Let's first work with the number -32.
This can be...
(8)(-4)
(-8)(4)
(16)(-2)
(-16)(2)
(32)(-1)
(-32)(1)
 
To provide an example...
The first FOIL would be...
(x+8)(x-4)
FIRST...(x)(x)=x2
OUTER...(x)(-4)=-4x
INNER...(8)(x)=8x
LAST...(8)(-4)=-32
x2+8x-4x-32
x2+4x-32
a=4
 
If I understand the question correctly, all integers are...
-31, -14, -4, 4, 14, 31
 

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