Factoring Calculator
Factorise expressions like 6x² − 7x − 3, 4a² − 9b² or 6x²y + 9xy², with every step shown and checked.
About the Factoring Calculator
Factorising rewrites an expression as a product. Always look for a common factor first. Then check for a difference of two squares, a² − b² = (a + b)(a − b). For a quadratic ax² + bx + c, split the middle term: find two numbers that multiply to ac and add to b, then factorise in pairs.
A quadratic with whole-number coefficients factorises with whole numbers only when its discriminant b² − 4ac is a perfect square. Otherwise use the quadratic formula for its roots.
The formula
ax² + bx + c = ax² + px + qx + c, where pq = ac and p + q = b
- a² − b²
- (a + b)(a − b)
- a² + 2ab + b²
- (a + b)²
Worked example
6x² − 7x − 3
- ac = −18; −9 × 2 = −18 and −9 + 2 = −7
- 6x² − 9x + 2x − 3
- 3x(2x − 3) + 1(2x − 3)
- = (3x + 1)(2x − 3)
Questions people ask
How do I check a factorisation?
Expand the brackets: you should get the original expression back. The Expand Brackets Calculator does this.
Can every quadratic be factored?
Over whole numbers, only when the discriminant b² − 4ac is a perfect square. Otherwise the roots are irrational or complex, and the quadratic formula gives them.