Factoring Calculator
Factor quadratics, binomials, and cubics with full step-by-step working. Enter an expression like x^2 + 5x + 6 below.
Worked examples
Here's how the calculator handles a few common patterns:
x^2 + 5x + 6
= (x + 3)(x + 2)
- Factor the quadratic x^2 + 5x + 6 by finding two numbers that multiply to 6 and add to 5, then factor by grouping: (x + 3)(x + 2).
2x^2 - 7x - 15
= (x - 5)(2x + 3)
- Factor the quadratic 2x^2 - 7x - 15 by finding two numbers that multiply to -30 and add to -7, then factor by grouping: (x - 5)(2x + 3).
x^2 - 9
= (x - 3)(x + 3)
- Factor the quadratic x^2 - 9 by finding two numbers that multiply to -9 and add to 0, then factor by grouping: (x - 3)(x + 3).
x^3 - 8
= (x - 2)(x^2 + 2x + 4)
- Recognize this as a difference of cubes: (1x)^3 - (2)^3, which factors as (px - q)(p^2x^2 ∓ pqx + q^2).
How this calculator factors an expression
- Factor out the greatest common factor (GCF) shared by every term, including any common power of the variable.
- For a quadratic ax² + bx + c, find two numbers that multiply to a×c and add to b, then split the middle term and factor by grouping (the "AC method"). This same process automatically catches differences of squares and perfect square trinomials.
- For a cubic, check first for a sum or difference of cubes (a³x³ ± b³). Otherwise, search for a rational root using the rational root theorem, divide it out, and factor the resulting quadratic the same way.
Looking for the factors of a specific whole number instead of an algebraic expression? Try the factor calculator or browse factors of a number.
Frequently asked questions
What kinds of expressions can this factoring calculator handle?
It factors polynomials in a single variable up to degree 3: linear expressions, quadratic trinomials and binomials (including differences of squares), and cubics (including sums and differences of cubes, and cubics with a rational root).
How do you factor a quadratic like x² + 5x + 6?
Find two numbers that multiply to give the constant term (6) and add to give the middle coefficient (5) - here, 2 and 3. Rewrite the middle term using those numbers, then factor by grouping to get (x + 2)(x + 3).
What if the expression does not factor?
Not every polynomial factors into integer or simple rational pieces. If it doesn't, the calculator shows the discriminant or rational-root check it used and explains why - the expression may still be solvable using the quadratic formula.
Does this handle factoring by grouping?
Yes. Quadratics with a leading coefficient greater than 1 (like 2x² - 7x - 15) are factored using the standard AC method and grouping, with each step shown.
Can it factor sum and difference of cubes?
Yes - expressions like x³ - 8 or x³ + 27 are recognized as a difference or sum of cubes and factored using the standard cube formulas.