Question

Find all integers k so that the trinomial can be factored 2m^2+km-5

Answer 1

The trinomial will come out to be

`(2m+a)(m+b)`
for some integers
`a` and
`b`.

We know that
`ab=-5` because the constant term is -5.

We also know that
`2bm+am=km\rightarrow2b+a=k`

Possibilities:
1.
`a=1,\ b=-5\rightarrow k=2b+a=-9`
2.
`a=5,\ b=-1\rightarrow k=2b+a=3`
3.
`a=-1,\ b=5\rightarrow k=2b+a=9`
4.
`a=-5,\ b=1\rightarrow k=2b+a=-3`

So
`k` can be 9, 3, -9, or -3.