Algebra
Factoring quadratics
Factoring rewrites a quadratic as a product of two binomials. For x² + bx + c, look for two numbers that multiply to c and add to b. When a ≠ 1, split the middle term using two numbers that multiply to ac.
Why it matters
Factored form reveals the roots instantly, which is what graphing, simplifying rational expressions and solving inequalities all depend on.
Worked example
Factor 6x² + 11x − 10
- 1Multiply a and c. 6 × (−10) = −60
- 2Find two numbers. 15 and −4 multiply to −60 and add to 11
- 3Split the middle term. 6x² + 15x − 4x − 10
- 4Factor in pairs. 3x(2x + 5) − 2(2x + 5) = (3x − 2)(2x + 5)
Answer: (3x − 2)(2x + 5)
Common mistakes
- Finding numbers that add correctly but multiply to c instead of ac when a ≠ 1.
- Forgetting to factor out a common factor first.
- Mismatching signs so the expansion gives the wrong middle term.
How to check your answer
- Expand your factors — you must recover the original expression exactly.
- If nothing works cleanly, the quadratic may not factor over the integers; use the formula.
Related topics
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