Factoring Calculator

Factor a Polynomial

Enter an expanded polynomial and the calculator will factor it within the supported algebra patterns.

Supported: integer coefficients, x only, expanded forms up to quadratic. Try x^2 + 5x + 6 or x^2 - 9.

  • Common monomial factor, such as 6x^2 + 9x
  • Difference of squares, such as x^2 - 9
  • Integer quadratic trinomials, such as x^2 + 5x + 6

Factoring result

Factored form Enter an expanded polynomial The method and check will appear after factoring.

What is Factoring?

Factoring rewrites an expanded polynomial as a product of simpler expressions. The factored form should multiply back to the original polynomial.

For example, x² + 5x + 6 can be factored as (x + 2)(x + 3). Factoring is useful for simplifying expressions and preparing equations for solving.

How Factoring Works

Follow these detailed steps:

  1. Step 1: Look for GCF First
    Check if all terms share a common factor. For 6x² + 9x, the GCF is 3x, giving 3x(2x + 3). Always factor this out first.
  2. Step 2: Identify the Pattern
    Determine if it's a difference of squares (a² - b²), perfect square trinomial, or general trinomial. Each has its own factoring method.
  3. Step 3: Factor Completely
    Continue until the remaining factors cannot be factored further within the supported pattern. Check your work by multiplying back out.

Common Factoring Patterns

a² - b² = (a - b)(a + b)

For quadratic trinomials, find factors that reproduce the leading term, constant term, and middle term when multiplied.

Example

Quadratic Factoring Example

Problem: Factor x² + 5x + 6

Solution:

  1. Find two numbers that multiply to 6 and add to 5.
  2. Those numbers are 2 and 3.
  3. Write the factors as (x + 2)(x + 3).
  4. Check: (x + 2)(x + 3) = x² + 5x + 6.

Quick Calculation Tips

  • Always check for GCF first - it makes the remaining factoring easier
  • Difference of squares: a² - b² = (a+b)(a-b) - memorize this pattern
  • For trinomials, look for factors that rebuild the middle term
  • Multiply the factors back out to verify the answer

Common Mistakes to Avoid

  • Stopping too early
    Continue factoring until no factor can be broken down further. (x² - 4) can be factored again.
  • Forgetting to check by multiplying
    Always verify your factoring is correct by multiplying the factors back together.

Frequently Asked Questions

What does factored form mean?

Factored form writes a polynomial as multiplied factors, such as (x + 2)(x + 3), instead of expanded form, such as x² + 5x + 6.

Why does this calculator reject parentheses?

Parentheses usually mean the expression is already in factored or grouped form. This tool expects an expanded polynomial so it can choose a factoring method.

What if a polynomial cannot be factored here?

It may be unfactorable over integer factors, or it may require a method outside this calculator's supported quadratic patterns.

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