# Polynomial factorization

Contents

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

14 exercises available

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

Learn how to write a monomial as a factor of two other monomials. For example, write 12x^3 as (4x)(3x^2).

Learn about common monomial factors and how to find the greatest common factor of two monomials. For example, find the greatest common factor of 6x^2y and 9xy^2 (answer: 3xy).

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 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 of 1. For example, factor x²+3x+2 as (x+1)(x+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).

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).

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.

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.