GCF Factoring

Algebra 1 · Axiom Academy

Find the greatest common factor of a polynomial's terms, pull it to the front, and write what remains in parentheses. 1. The GCF Is the Shared Piece The greatest common factor of a set of terms is the biggest "piece" they all contain. Every one of 12, 18, 24 can be split into a group of 6 times something — so a 6 can be lifted out of each. Press play and watch the shared 6 break out of all three. For a reliable method, break each number into its prime factors and keep only the primes they have in common . Watch 24 = 2·2·2·3 and 36 = 2·2·3·3 line up; the primes that pair off in both columns slide together and multiply into the GCF. 36: 1, 2, 3, 4, 6, 9, 12 , 18, 36 The largest factor in both lists is 12 . Take the lowest power of each shared prime: two 2's and one 3. A variable is just a stack of identical letters: x^3 is three x 's multiplied together. A factor can only be pulled from every term, so for each letter the GCF keeps the smallest exponent that appears. Watch the x -stacks and y -stacks shrink down to the shortest one in each row. — smallest of each letter ( x^1 and y^3 ). — b is missing from a^3 , so b drops out entirely. 4. Pulling the GCF to the Front Once you have the GCF, factor it out: divide every term by the GCF and write what is left inside parentheses. Watch 12x^3 + 18x^2 — the GCF 6x^2 slides out to the front, each term divides, and the leftovers 2x and 3 drop into the parentheses. Numbers ; variables . GCF =6x^2 .

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