Factoring polynomials

Question

When factoring a polynomial in the form ax^2 + bx+ c, where a, b and c are positive real numbers, should the signs in the binomials be both positive, negative or one of each? Create an example to verify your claim

Answer 1

When c is positive the signs on the binomials are either both positive or both negative. The sign on b determines which.

x^2 + 8x + 15 = (x + 5)(x + 3)

x^2 - 8x + 15 = (x - 5)(x - 3)

When c is negative the signs on the binomials are one positive and one negative. The sign on b determines which is larger.

x^2 + 2x - 15 = (x + 5)(x - 3)

x^2 - 2x - 15 = (x - 5)(x +3)