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

find all integers for "a" in which x2+ax-32 can be factored. Explain how you arrived at your conclusion.

### 2 Answers by Expert Tutors

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
1
-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.
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
0
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