How to Factor Polynomials (With Examples)

Factoring a polynomial means rewriting it as a product of simpler polynomials. It is the reverse of expanding brackets, and it is the usual first step in solving polynomial equations.

Start with the common factor

Always look first for a factor shared by every term. For example, 6x² + 9x = 3x(2x + 3).

Quadratic trinomials

For x² + 5x + 6, find two numbers that multiply to 6 and add to 5. Those numbers are 2 and 3, so x² + 5x + 6 = (x + 2)(x + 3).

Difference of two squares

a² − b² = (a − b)(a + b). For example, x² − 9 = (x − 3)(x + 3).

Grouping

For four terms, group them in pairs and factor each pair. For example, x³ + 2x² + 3x + 6 = x²(x + 2) + 3(x + 2) = (x² + 3)(x + 2).

Check

Expand your factors. If you do not get the original polynomial back, one of the factors is wrong.

Learn more

For a video explanation of this topic, see Khan Academy Algebra course.