factor.

Factoring Calculator with Free Steps

One polynomial · integer coefficients · total degree ≤4 · up to 2 of x/y/z · + − * ^ ( )

Examples & math keys

Use ^ for powers; 5x works too. Whole numbers such as 48 also work. Limits: 220 characters and coefficient magnitude up to 1 trillion.

All steps are free — no sign-up, no paywall.

Worked example

FACTORED FORM
(x+2)(x+3)

from x^2+5x+6

✓ Checked

Show steps

Trinomial x^2+bx+c

  1. Find the sum and product

    2+3=5; 2*3=6

    The middle coefficient is the sum; the constant is the product.

  2. Write the factors

    x^2+5x+6=(x+2)(x+3)

    Expanding these factors reproduces all three terms.

Check by expanding

(x+2)(x+3)=x^2+3x+2x+6=x^2+5x+6

The factors expand back to the original expression. ✓

Why factoring matters

Factoring reveals the pieces that multiply to make an expression. It helps you simplify algebra, compare equivalent forms, and see patterns that are easy to miss in an expanded polynomial. The value stays the same; the structure becomes clearer.

Start with a shared factor, then look for a familiar pattern. This skill also helps when you later simplify fractions or solve equations. Use the steps to understand each move, then multiply the factors back to check your work. A prime polynomial is a valid conclusion, not a mistake. See factoring trinomials.

Common mistakes

  • Wrong signs: check both the sum and product of a factor pair.
  • Missing the GCF: take out the greatest common factor before applying a pattern.
  • Losing a negative: dividing a group by a negative factor changes every sign inside it.
  • Skipping the check: expand every factor and compare all terms with the original expression.

FAQ

How to calculate factoring?

Combine like terms, then take out the greatest common factor. Look for a difference of squares, a trinomial, or terms that share a group; enter the expression above to see which method fits.

How do you check your factoring?

Multiply the factors and combine like terms. Every coefficient, variable, exponent, and sign must match the original expression; see Show steps for the expansion check.

How to solve factoring step by step?

Start with the common factor, apply a matching pattern, and check each remaining factor. This tool factors expressions; solving an equation is a separate task, and a prime polynomial has no further integer polynomial factors.