Factoring 12x³ + 18x² - 6x

Algebra 1 · Axiom Academy

Factor a polynomial completely by pulling out the greatest common factor first. Factor the polynomial 12x^3 + 18x^2 - 6x completely. Start by finding the greatest common factor (GCF) of all three terms. Nice work. You factored a polynomial completely by leading with the GCF. Keep these steps in hand: Always start with the GCF: pull out the greatest common factor of every term before trying anything else. Coefficients and variables separately: GCF = (GCF of the coefficients) times (the lowest power of each shared variable). Then check for more factoring: after the GCF comes out, test whether the leftover polynomial factors again. Verify by multiplying back: distribute your factors to confirm you land on the original expression. Result: 12x^3 + 18x^2 - 6x = 6x(2x^2 + 3x - 1) , and 2x^2 + 3x - 1 is prime over the integers. The GCF method works on any polynomial — always look for common factors first before reaching for other techniques.

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