Question

Factor the expression
5y^2+12y-32

Answer 1

If there are integer solutions, you know the constant terms of the binomials which can be called a and b must equal -32 when multiplied. Since 5 is prime we know the coefficients on y are 5 and 1. So we have

(5y + a)(y + b)

we know ab=-32, so exactly one of a, b is negative.

Answer 2

The coefficient on the term of y to the first power must be the sum of 5b and a.