Polynomial factorization

Learn how to write polynomial expressions as the product of linear factors. For example, write x^2+3x+2 as (x+1)(x+2).
16 exercises available

Learn how to evaluate expressions with variables whose values are unknown, by using another information about those variables. For example, given that a+b=3, evaluate 4a+4b.

Learn how to factor quadratic expressions with a leading coefficient other than 1. For example, factor 2x²+7x+3 as (2x+1)(x+3).

Learn how to factor quadratic polynomials of the form ax^2+bx+c as the product of two linear binomials. For example, write x^2+3x-10 as (x+5)(x-2). Learn how to identify these forms in more elaborate polynomials that aren't necessarily quadratic. For example, write x^4-4x^2-12 as (x^2+2)(x^2-6).

There are a lot of methods to factor quadratics, which apply on different occasions and conditions. Now that we know all of them, let's think strategically about which of them is useful for a given quadratic expression we want to factor.

Factor polynomials of various degrees using factorization methods that are based on the special product forms "difference of squares" and "perfect squares." For example, factor 25x⁴-30x²+9 as (5x²-3)².