How can finding the factor pairs of the constant in a trinomial help me factor the trinomial???
If you are given a quadratic in the form:
$\displaystyle x^2+ax+b$
Finding the factor pair of b whose sum is a, will easily allow you to factor the quadratic.
Suppose $\displaystyle b=cd$ where $\displaystyle a=c+d$, then we may write:
$\displaystyle x^2+ax+b=(x+c)(x+d)$
For the more general quadratic:
$\displaystyle ax^2+bx+c$
we want to find the factor pair of $\displaystyle ac$ whose sum is $\displaystyle b$.