Factoring Glossary

Here is a glossary of terms that are commonly used in the context of factoring.

difference of squares

A difference of squares is a difference where both terms are squares: \(A^2 - B^2\). In this case, we can always factor, since \(A^2 - B^2 = (A - B)(A + B)\).

FOIL

FOIL stands for First, Outer, Inner, Last. It represents the four products that you get when expanding a product of binomials: \((a+b)(c+d) = ac + ad + bc + bd\).

monic

A polynomial is called monic if its leading coefficient is 1. For quadratics of the form \(ax^2 + bx + c\), this means \(a = 1\).

sum/difference of cubes

A sum/difference of cubes is a sum/difference where both terms are cubes: \(A^3 + B^3\) or \(A^3 - B^3\). In these cases, we can always factor, since \(A^3 \pm B^3 = (A \pm B)(A^2 \mp AB + B^2)\).