Factoring by Grouping

Algebra 1 · Axiom Academy

A four-term polynomial that fits no standard pattern can still be factored — by splitting it into two pairs and pulling out what they share. 1. The Idea: Pair, Pull, Share Take a generic four-term polynomial. Split it into two pairs , factor the greatest common factor (GCF) out of each pair, and — if you grouped well — both pairs are left multiplying the same binomial . That shared binomial is the key: factor it out of the whole thing. Pair 1 gives x ; pair 2 gives y — both leave (a+b) Factor the shared (a+b) out front Factor the polynomial below. Watch the animation build the grouping, then read each written step underneath. Sometimes the binomials come out almost matching but with flipped signs. The fix: factor a negative GCF out of the second pair so the binomial flips into alignment. The order the terms arrive in is not sacred. If the obvious pairing has no common factor, reorder the terms so each new pair shares something. Factoring and expanding are inverses, so every factorization carries its own answer key: multiply the two binomials back out. If you land on the original polynomial, you are right. A quick checklist for factoring by grouping: Do you have exactly four terms? Can you split them into two pairs? Does each pair have a GCF to pull out? Do the leftover binomials match (or can a negative / a reorder make them)? Did you multiply back to confirm?

This is the written version of the interactive lesson above. See the full Algebra 1 course.