Why can't some quadratics be factored?

If the discriminant is not a perfect square, the roots are irrational or complex and the quadratic does not factor over the integers.

Factoring Calculator

Factor any polynomial with a clear strategy: pull out the greatest common factor, recognize special patterns, and use the Rational Root Theorem for higher degrees. The factored form is verified by expanding it back.

How to use the factoring calculator

Enter the polynomial.
Press Factor to see the strategy and the complete factorization.

Examples

x³ − 2x² − 9x + 18

Answer: (x − 2)(x − 3)(x + 3)

4x² − 25

Answer: (2x − 5)(2x + 5)

Formulas

Difference of Squares

a^{2} - b^{2} = (a - b) (a + b)

Sum and Difference of Cubes

a^{3} \pm b^{3} = (a \pm b) (a^{2} \mp ab + b^{2})