The trinomial will come out to be
[tex](2m+a)(m+b)[/tex]
for some integers [tex]a[/tex] and [tex]b[/tex].
We know that [tex]ab=-5[/tex] because the constant term is -5.
We also know that [tex]2bm+am=km\rightarrow2b+a=k[/tex]
Possibilities:
1. [tex]a=1,\ b=-5\rightarrow k=2b+a=-9[/tex]
2. [tex]a=5,\ b=-1\rightarrow k=2b+a=3[/tex]
3. [tex]a=-1,\ b=5\rightarrow k=2b+a=9[/tex]
4. [tex]a=-5,\ b=1\rightarrow k=2b+a=-3[/tex]
So [tex]k[/tex] can be 9, 3, -9, or -3.
