If the trinomial 2x^2 + sx + 2 can be factored, what value(s) of "s" are possible?

Question

Im studying for a midterm and don't know how to do this.

Answer 1

FOIL (first outside, inside last) factors of 2 are 1,2 or -1,-2.

2x^2 + sx + 2
s could be 0. 2x^2+2 factors into 2(x^2+1)
s could be 5. (2x + 1)(x + 2)
s could be 4. (2x+2)(x+1) = 2(x+1)(x+1)
s could be -5. (2x-1)(x-2)
s could be -4. (2x-2)(x-2) = 2(x-1)(x-1)

The way to do it is to find the factors for the first and last term, and then see what the possibilities are for the middle term.

Answer 2

It could be factored (2x+1)(x+2), so s would be 5x (product of the outside numbers+product of the inside numbers)

Or it factors (2x+2)(x+1) so s would be 4x

So 5 or 4 equal s.