Algebra 1 Intermediate

Factoring Polynomials

Factor any polynomial completely using GCF, difference of squares, trinomials, and sum/difference of cubes.

Live Calculator · Step-by-Step · Algebra
Polynomial Input
Use ^ for exponents. Examples: x^2-9, x^3-27, x^3+x^2-4x-4
Examples
Factored Form
Enter a polynomial above and press Factor Polynomial to see the factored form, method used, and a verification check.
Factored Form
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Method Used
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Verification (expand back)
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Step-by-Step Factoring
Factor Tree
Teal nodes · Gold labels · Arrow connections
Factoring Strategy
Step 1 → GCF · Step 2 → Pattern → Step 3 → Verify

1. Always factor out GCF first. Find the greatest common factor of all terms and pull it out. This simplifies everything that follows.

2. Count terms and identify the pattern:

• 4 terms → Try grouping: split into two pairs, factor each pair, then factor the common binomial.

• 2 terms → Check difference of squares (a²−b²) or sum/difference of cubes (a³±b³).

• 3 terms → Check perfect square trinomial (a²±2ab+b²) first, then use the AC method for ax²+bx+c.

If a trinomial has a leading coefficient > 1, use the AC method: multiply a·c, find two numbers that multiply to ac and add to b, then split the middle term and group.
Special Formulas
a² − b² = (a + b)(a − b)
a² + 2ab + b² = (a + b)²
a² − 2ab + b² = (a − b)²
a³ − b³ = (a − b)(a² + ab + b²)
a³ + b³ = (a + b)(a² − ab + b²)
  • Sum of squares (a²+b²) does NOT factor over real numbers.
  • Difference of squares requires both terms to be perfect squares.
  • For cubes: identify a and b, then apply the formula directly.
  • Always check if the result can be factored further (factor completely).
Related Calculators
Expand & Simplify
Expand and simplify polynomial expressions with step-by-step distribution
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Factoring GCF
Factor out the greatest common factor from polynomial terms step by step
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Factoring Trinomials
Factor ax²+bx+c trinomials using the AC method and grouping technique
Open tool →
Difference of Squares
Factor a²−b² = (a+b)(a−b) with step-by-step identification of a and b
Open tool →

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