Factoring Polynomials

Greatest Common Factor (GCF)

Factor out the largest common expression.

Example: $6x^3 + 9x^2 = 3x^2(2x + 3)$

Factoring Trinomials

For $x^2 + bx + c$, find two numbers that multiply to $c$ and add to $b$.

Example: $x^2 + 7x + 12 = (x + 3)(x + 4)$

Difference of Squares

$a^2 - b^2 = (a + b)(a - b)$

Example: $x^2 - 25 = (x + 5)(x - 5)$

Perfect Square Trinomials

$a^2 + 2ab + b^2 = (a + b)^2$

Example: $x^2 + 6x + 9 = (x + 3)^2$