Enter a quadratic
Use the expression box or enter three coefficients. Fractions and decimals are accepted.
Formula used
Quadratic form: ax² + bx + c
X product: a × c
Pair rule: mn = ac and m + n = b
Discriminant: Δ = b² − 4ac
The X method finds two numbers. Their product equals ac. Their sum equals b.
Those numbers split the middle term. Grouping then reveals two matching binomials. Multiplication verifies the final factors.
How to use
- Enter a complete quadratic expression or three coefficients.
- Select the preferred method and answer format.
- Choose the decimal precision and visible solution details.
- Press “Factor quadratic” to calculate the result.
- Copy, print, or download the completed solution.
Example data
| Expression | ac | Selected pair | Factored form |
|---|---|---|---|
| 6x² + 11x + 3 | 18 | 9 and 2 | (3x + 1)(2x + 3) |
| x² − 5x + 6 | 6 | −2 and −3 | (x − 2)(x − 3) |
| 2x² − 8x | 0 | 0 and −8 | 2x(x − 4) |
| x² − 25 | −25 | 5 and −5 | (x + 5)(x − 5) |
Recent calculations
| Time | Expression | Result |
|---|---|---|
| No saved calculations. | ||
Frequently asked questions
What is the X method?
It is a factoring shortcut. It uses product ac and sum b. The pair splits the middle term.
Can the calculator use negative coefficients?
Yes, negative values are supported. Negative factor pairs are checked automatically. Signs remain visible throughout each step.
Can I enter fractions?
Yes, enter values like 3/4. The calculator scales coefficients to integers. The outside rational factor remains exact.
What happens when no integer pair works?
The calculator reports that result. It then provides available quadratic roots. Complex roots can also appear.
Why is the greatest common factor removed first?
Removing it simplifies the trinomial. Smaller coefficients make factor pairs clearer. The common factor stays outside.
Does it detect perfect-square trinomials?
Yes, a zero discriminant identifies them. Repeated roots are shown once. Repeated factors remain easy to recognise.
Does it handle difference of squares?
Yes, common square patterns are detected. The factorisation still uses valid binomials. The pattern label explains it.
How are answers verified?
The calculator compares expanded coefficients. Matching coefficients confirm the factorisation. The original expression is restored.
Can I use another variable?
Yes, enter one alphabetic character. Expressions can also reveal their variable. Results preserve that chosen symbol.