Polynomial Factoring Calculator
This free tool factors quadratic trinomials of the form ax2 + bx + c. Enter the coefficients to see the roots, the factored form, and the step-by-step working, including the discriminant, so you can check your method, not just the answer.
Enter values — the result will show live here.
How to use
- Write the expression in the form ax² + bx + c and enter a, b, c. For example, for x² + 5x + 6: a=1, b=5, c=6.
- The factored form and both roots will appear in the result; the middle step (two numbers whose sum is b and product is a x c) will also be shown.
- Check the discriminant line — a negative value means no real roots, and a = 0 means the expression is linear, not quadratic.
Tips
- Try a = 1, b = 5, c = 6 first to see a clean example: (x + 2)(x + 3).
- A negative discriminant means no real factors — the roots are complex numbers.
- Always verify the answer by expanding the factored form back out.
Note: Discriminant D = b² - 4ac. If D < 0, real factors are not formed (roots are complex). If a = 0, the expression is no longer quadratic.