Factoring Calculator
Enter a, b, and c below to instantly factor ax² + bx + c.
For ax² + bx + c
Step by Step
- 1. Look for two numbers— that multiply to c = 6 and add to b = -5
- 2. Found them— -3 × -2 = 6, and -3 + -2 = -5
- 3. Write the factored form— (x − 3)(x − 2)
How Factoring Works
Every quadratic's roots come from the quadratic formula. Once you have both roots, the factored form follows directly.
Worked example
Factor x² − 5x + 6.
Roots: x = 3 and x = 2.
x² − 5x + 6 = (x − 3)(x − 2)
Keep going
- Factoring only works cleanly when a quadratic's roots are whole numbers; the quadratic formula calculator solves any quadratic, including ones that don't factor nicely. Quadratic Formula Calculator
- Factoring finds a polynomial's roots directly; synthetic division checks whether a specific value is a root by dividing it out, and the synthetic division calculator shows that process step by step. Synthetic Division Calculator
Frequently Asked Questions
How do you factor a quadratic?
Find the two roots using the quadratic formula, then write the expression as a(x − r₁)(x − r₂), where r₁ and r₂ are those roots.
What does it mean if a quadratic doesn't factor?
If the discriminant (b² − 4ac) is negative, the roots are complex numbers, and the expression can't be factored into two simple (x − r) terms using only real numbers.
How is factoring different from solving a quadratic equation?
Solving finds the values of x that make the expression equal zero. Factoring rewrites the same expression as a product of simpler terms — the roots you'd get from solving are exactly the numbers that show up in the factored form.
Related Calculators
- Quadratic Formula Calculator — Algebra
- Log Calculator — Algebra
- Exponent Calculator — Algebra
- System of Equations Calculator — Algebra