The architect must factor several trinomials the are of the form x2- mx + n, where m & n are whole numbers greater than zero. She wonders if any of these trinomials factor as (x+a)(x+b), where a > 0 and b < 0. Is this possible? Why or why not?

Question

I do not understand how to figure this out, at first I was thinking no this isn't possible because m and n are greater than zero and a>0 is less than? But then it made no sense to me... :/

Answer 1

(x+a)(x+b) = x^2 + (a+b)x + ab

If a>0 and b<0, then ab<0 so there's no way that n can be positive if a and b have different signs.