# 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).

This course contains 12 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.

**Polynomial Remainder Theorem**

The polynomial remainder theorem allows us to easily determine whether a linear expression is a factor of a given polynomial. Learn exactly what the theorem means, practice using it, and learn about its proof.

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Rating | Not enough ratings |
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Length | 12 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

## Get a Reminder

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Rating | Not enough ratings |
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Length | 12 segments |

Starts | On Demand (Start anytime) |

Cost | Free |

From | Khan Academy |

Download Videos | On all desktop and mobile devices |

Language | English |

Subjects | Mathematics |

Tags | Math |

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