Factoring Calculator

Factor polynomials (quadratic, cubic, etc.) using GCF, difference of squares, and more. Learn factoring methods with step-by-step explanations for algebra students.

100% FreeStep-by-step SolutionsMultiple Methods

Polynomial Factoring Calculator

Enter a polynomial expression to factor (e.g., x^2 + 5x + 6, 2x^2 - 8, x^3 - 3x^2 + 2x)

Polynomial Expression *

Use format: x^2 + 5x + 6, 2x^3 - 8x^2 + 6x, etc. Variable can be x, y, z, etc.

Factoring Examples

Click on any example to automatically fill the calculator

AC Method

x^2 + 5x + 6

Simple quadratic factoring

Difference of Squares

x^2 - 9

Difference of squares

Perfect Square

x^2 + 6x + 9

Perfect square trinomial

GCF + Factoring

2x^2 + 8x + 6

Quadratic with GCF

GCF Method

3x^3 - 12x^2 + 12x

Cubic with GCF

GCF + Difference of Squares

4x^2 - 16

Difference of squares with GCF

What is Factoring?

Factoring is the process of breaking down a polynomial into a product of simpler polynomials (factors). It's the reverse of polynomial multiplication and is fundamental in algebra.

Why Factor Polynomials?

Solve Equations: Factor to find zeros using Zero Product Property
Simplify Expressions: Cancel common factors in fractions
Graph Functions: Find x-intercepts and behavior
Advanced Topics: Partial fractions, calculus applications

Example: $x^2 - 5x + 6 = (x - 2)(x - 3)$
This means x² - 5x + 6 = 0 has solutions x = 2 and x = 3

Common Factoring Methods

1. Greatest Common Factor (GCF)

Factor out the largest common factor first.

6x² + 9x = 3x(2x + 3)

2. Difference of Squares

$a^2 - b^2 = (a + b)(a - b)$

x² - 9 = (x + 3)(x - 3)

3. Perfect Square Trinomial

$a^2 ± 2ab + b^2 = (a ± b)^2$

x² + 6x + 9 = (x + 3)²

4. AC Method (Grouping)

For ax² + bx + c, find factors of ac that add to b.

2x² + 7x + 3 = (2x + 1)(x + 3)

Applications of Factoring in Algebra

Solving Equations

Quadratic equations: ax² + bx + c = 0
Zero Product Property: if ab = 0, then a = 0 or b = 0
Finding roots and x-intercepts
Higher-degree polynomial equations

Simplifying Expressions

Reducing rational expressions
Canceling common factors
Simplifying complex fractions
Partial fraction decomposition

Function Analysis

Finding zeros and y-intercepts
Graphing polynomial functions
Determining domain restrictions
Optimization problems

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