College Algebra (10th Edition)

$(x-2)(x+4)$
RECALL: A trinomial of the form $x^2+bx+c$ can be factored if there are integers $d$ and $e$ such that $c=de$ and $b=d+e$. The trinomial's factored form will be: $x^2+bx+c=(x+d)(x+e)$ The given trinomial has $b=2$ and $c=-8$. Note that $-8=(-2)(4)$ and $2=(-2)+4$. This means that $d=-2$ and $e=4$ Thus, the factored form of the trinomial is: $=[x+(-2)] (x+4) \\=(x-2)(x+4)$