Factorization

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This course is a part of Algebra I, a 21-course Topic series from Khan Academy.

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

This course contains 11 segments:

Introduction to factorization

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

Factoring monomials

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

Factoring polynomials by taking common factors

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).

Evaluating expressions with unknown variables

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.

Factoring quadratics intro

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

Factoring quadratics by grouping

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

Factoring polynomials with quadratic forms

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).

Factoring quadratics: Difference of squares

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).

Factoring quadratics: Perfect squares

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.

Strategy in factoring quadratics

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.

Factoring polynomials with special product forms

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.