GCF-FIRST
Always factor out the Greatest Common Factor first!
Before anything else — look for GCF.
DOTS
\(a^2 - b^2 = (a+b)(a-b)\)
Difference Of Two Squares → two opposite signs
PST
\(a^2\pm 2ab+b^2=(a\pm b)^2\)
Perfect Square Trinomial → check middle term = 2ab
SUM-DIFF-CUBES
\(a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)\)
SOAP: Same · Opposite · Always Positive
AC-METHOD
For \(ax^2+bx+c\): find factors of \(ac\) that add to \(b\)
Multiply ends (a·c), find pair, split middle term
GROUPING
4 terms → group in pairs → factor each → pull common binomial
2+2 split is the most common grouping pattern