factoring by grouping

Splitting a four-term expression into pairs, each with its own factorable GCF.

Factoring by grouping handles four-term expressions: pair the terms, factor the GCF out of each pair, and if a common binomial factor remains, extract it. Also the standard technique for factoring $ax^2+bx+c$ once the middle term is split via the AC method (find factors of $ac$ summing to $b$ , rewrite $bx$ as their sum, then group).

Examples

$x^3+3x^2+2x+6 = x^2(x+3)+2(x+3) = (x^2+2)(x+3)$ .