Expert: Richard J. Raridon - 7/21/2006

Question
Hello
I am having some difficulty with the following problem.

How do you find all positive and negative integers b for which the following polynomial can be factored:  2h^2 + bh - 15

Answer
The two factors have to be of the form (2h-a) and (h+c).
If you multiply those together you get 2h^2+(2c-a)h -ac.
So you can see that ac = 15 and (2c-a) = b.  The only factors of 15 are 3 and 5 or 1 and 15.  So you have 4 possibilities for b:
a=3, c=5, b=7
a=5, c=3, b=1
a=15,c=1, b=-13
a=1,c=15, b=29