Polynomial Factorizer
Factor or solve a quadratic expression ax² + bx + c using the discriminant and quadratic formula.
Category: Calculators
When to use?
Use it to solve x² - 5x + 6, check roots of a quadratic graph, or verify factorization in algebra homework.
How to use
- Enter coefficients a, b, and c.
- The discriminant b² - 4ac is evaluated.
- Review the factored form or root information.
Input Explanation
Enter the coefficients for ax² + bx + c. If a is 0, the expression is treated as linear.
Calculation Basis
It applies x = (-b ± √(b² - 4ac)) / 2a. When roots are simple integers, it can present a factored form such as (x - 2)(x - 3).
Usage Examples
- Algebra checks - Confirm a quadratic factorization result.
- Graph intercepts - Find where a quadratic graph crosses the x-axis.
Examples
- x² - 5x + 6 → (x - 2)(x - 3)
- 2x² - 8x + 6 → 2(x - 1)(x - 3)
- x² + 1 has complex roots and cannot be factored over the real numbers
FAQ
What if the discriminant is negative?
There are no real roots. The tool reports complex roots instead of a real-number factorization.
Can I use decimal coefficients?
Yes. Decimal coefficients are accepted, though displayed factors may be approximate.
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