Factoring Calculator

Factor quadratic expressions step by step.

What is Factoring?

Factoring means rewriting an expression as a product of simpler expressions.

Example: x² + 5x + 6 = (x + 2)(x + 3)

How to Factor x² + bx + c

1. Find two numbers that:
2. Multiply to give c
3. Add to give b
4. Write as factors: (x + p)(x + q)

Factoring Steps

For x² + 5x + 6: 1. Need two numbers that multiply to 6 and add to 5 2. Numbers are 2 and 3 (2 × 3 = 6, 2 + 3 = 5) 3. Factors: (x + 2)(x + 3)

Types of Factoring

Greatest Common Factor (GCF) - Factor out common terms first - Example: 2x² + 4x = 2x(x + 2)

Difference of Squares - a² - b² = (a + b)(a - b) - Example: x² - 9 = (x + 3)(x - 3)

Trinomial Factoring - x² + bx + c = (x + p)(x + q) - Example: x² + 7x + 12 = (x + 3)(x + 4)

Why Factor?

Factoring helps you: - Solve quadratic equations - Simplify expressions - Find roots and zeros - Graph parabolas

Common Questions

What does it mean to factor an expression?

Factoring means rewriting an expression as a product of simpler expressions. For example, x² + 5x + 6 factors to (x + 2)(x + 3).

How do you factor a quadratic?

To factor x² + bx + c, find two numbers that multiply to c and add to b. These become the constants in your factors: (x + p)(x + q).