Factoring Calculator

Factor quadratic trinomials and polynomials. Enter coefficients for ax² + bx + c and get the factored form with step-by-step explanations.

Factor Quadratic Trinomial

Enter coefficients for: ax² + bx + c

Coefficient a:

Coefficient b:

Coefficient c:

How to Factor Quadratics

For a quadratic ax² + bx + c, we find numbers p and q such that:

ax² + bx + c = (dx + e)(fx + g)

Factoring Methods

Method 1: AC Method (for a = 1)

For x² + bx + c:

Find two numbers that multiply to c and add to b
Write the factors: (x + p)(x + q)

Method 2: AC Method (for a ≠ 1)

For ax² + bx + c:

Calculate a × c
Find two numbers that multiply to a×c and add to b
Split the middle term and factor by grouping

Special Cases

Difference of squares: a² - b² = (a+b)(a-b)
Perfect square: a² ± 2ab + b² = (a ± b)²
GCF: Always factor out the greatest common factor first

Examples

Example 1: Simple Trinomial

Factor: x² + 5x + 6

Find numbers: 2 × 3 = 6 and 2 + 3 = 5

(x + 2)(x + 3)

Example 2: Negative Coefficients

Factor: x² - x - 6

Find numbers: -3 × 2 = -6 and -3 + 2 = -1

(x - 3)(x + 2)

Example 3: Non-Monic

Factor: 2x² + 7x + 3

AC = 6, find 1 and 6

Split: 2x² + x + 6x + 3

(2x + 1)(x + 3)

Example 4: Difference of Squares

Factor: x² - 9

Recognize: x² - 3²

(x + 3)(x - 3)

Example 5: Perfect Square

Factor: x² - 10x + 25

Recognize: x² - 2(5)(x) + 5²

(x - 5)²