Josh Liljenquist

Algebra calculator

Factoring Calculator

Enter a polynomial expression to factor it step by step. The calculator identifies supported factoring methods, returns the factored form, and verifies the result by expansion.

By

Integer factoringSteps shownExpansion verified

Enter a polynomial

Use x² or x^2. Integer coefficients, spaces, and implied multiplication are supported.

Enter a polynomial and select Factor.

How to factor a polynomial

First combine like terms and extract any greatest common factor. Then apply a pattern such as a difference of squares or find integer binomials whose product recreates the polynomial.

Greatest common factor

Every term in 6x² + 12x contains 6x, so the expression factors as 6x(x + 2).

Difference of squares

a² − b² = (a − b)(a + b). Therefore x² − 9 = (x − 3)(x + 3).

Factoring trinomials

For x² + 5x + 6, find two integers with product 6 and sum 5: 2 and 3. The factored form is (x + 2)(x + 3).

Factoring quadratics

For 2x² + 7x + 3, the integer binomials (2x + 1)(x + 3) expand to the original coefficients.

Factoring examples

  • x² + 6x + 9 = (x + 3)²
  • x² − 9 = (x − 3)(x + 3)
  • 6x² + 12x = 6x(x + 2)

What if a polynomial cannot be factored?

If no integer binomial factorization exists, the result says “Prime over the integers.” This version supports one-variable polynomial expressions in x up to degree 2 with integer coefficients; it rejects unsupported functions and malformed input instead of guessing.

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