Factoring Calculator
Type a polynomial and this calculator factors it into brackets: common factors, quadratics, difference of squares and cubics.
Use ^ for powers, e.g. x^2 - 9 or 2x^3 - 8x. Numbers like 84 are split into prime factors.
What is factoring?
Factoring (or factorising) is expanding brackets in reverse. Expanding turns (x + 2)(x + 3) into x² + 5x + 6; factoring starts from x² + 5x + 6 and finds the brackets that multiply to give it. Each bracket is a factor, just as 3 and 4 are factors of 12.
It matters because a product is easy to reason about. If (x + 2)(x + 3) = 0, then one of the brackets must be zero, so x = −2 or x = −3. That is how most quadratic equations are solved at GCSE, and factoring is also how algebraic fractions are simplified: a factor that appears on the top and the bottom cancels.
Not every expression factors neatly. x² + x + 1 has no factors with whole numbers (or even real numbers), and the calculator will leave it as it is. When a quadratic won’t factor, use the quadratic formula instead.
How to factor by hand
- Take out any common factor first: 2x² + 6x = 2x(x + 3).
- Check for a difference of two squares: x² − 25 = (x + 5)(x − 5).
- For a quadratic x² + bx + c, find two numbers that multiply to c and add to b.
- Check by multiplying the brackets back out.
Exemple résolu
Factor x² + 7x + 12: the numbers 3 and 4 multiply to 12 and add to 7, so x² + 7x + 12 = (x + 3)(x + 4).
To go the other way, use the Simplify Calculator; to solve a quadratic, use the quadratic formula in the Formules mathématiques calculator.
Foire aux questions
What does factoring mean?
Writing an expression as a product of simpler ones. x² + 5x + 6 factors to (x + 2)(x + 3), because multiplying those brackets out gives back x² + 5x + 6.
How do you factor a quadratic?
For x² + bx + c, find two numbers that multiply to c and add to b. For x² + 5x + 6 they are 2 and 3, so it factors to (x + 2)(x + 3).
What is the difference of two squares?
a² − b² = (a + b)(a − b). So x² − 9 = (x + 3)(x − 3).
Can it factor numbers too?
Yes: type a whole number like 84 and it is split into its prime factors (2² × 3 × 7).
