Factoring Calculator
This calculator factors quadratic expressions of the form ax² + bx + c. If the quadratic factors over the integers, it displays the factored form. If not, it provides the roots using the quadratic formula.
Factoring quadratics
Form: ax² + bx + c
Factored: (px + q)(rx + s)
If not factorable, use quadratic formula
Factoring: frequently asked questions
How do I factor a quadratic?
Find two numbers that multiply to a*c and add to b. Then factor by grouping or use the quadratic formula if not factorable.
What if the quadratic doesn't factor nicely?
If no integer factors exist, use the quadratic formula to find the roots. The calculator displays both the factored form and roots.
What does 'prime' mean in factoring?
A polynomial is prime if it cannot be factored into non-trivial polynomials with rational coefficients.
How do I check if my factorization is correct?
Multiply the factors together using FOIL (First, Outer, Inner, Last). You should get the original polynomial.
Can all quadratics be factored?
Over the integers, no. However, all quadratics can be solved using the quadratic formula, which gives either rational or irrational roots.
Methodology
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026.