# Factorization

Contents

Factorization is the decomposition of an object (for example, a number, a polynomial) into a product of other objects, or factors, which when multiplied together give the original. In this chapter we will learn about methods of factorization.

7 exercises available

Learn what factorization is all about, and warm-up by factoring some monomials.

Learn how to take a common monomial factor out of a polynomial expression. For example, write 2x^3+6x^2+8x as (2x)(x^2+3x+4).

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

Learn how to factor quadratics that have the "difference of squares" form. For example, write x²-16 as (x+4)(x-4). Learn how to identify this form in more elaborate expressions. For example, write 4x²-49 as (2x+7)(2x-7).

Learn how to factor quadratics that have the "perfect square" form. For example, write x²+6x+9 as (x+3)². Learn how to identify these forms in more elaborate expressions. For example, write 4x²+28x+49 as (2x+7)².

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