Factoring Quadratics
How to Factor Quadratics
Factoring a quadratic means rewriting it as a product of simpler expressions. For x² + bx + c, you are looking for two numbers that multiply to c and add to b.
What does it mean to factor a quadratic?
A factored form such as (x + p)(x + q) shows the multiplication hidden inside the quadratic. Expanding the brackets returns x² + (p + q)x + pq.
How to factor x² + bx + c
- Check for a greatest common factor first.
- Find two numbers that multiply to c.
- Choose the pair that adds to b.
- Write the two binomial factors.
- Expand your answer to check it.
Worked example
Factor x² + 11x + 24
- Factor pairs of 24 include 1 and 24, 2 and 12, 3 and 8, and 4 and 6.
- 3 × 8 = 24.
- 3 + 8 = 11.
x² + 11x + 24 = (x + 3)(x + 8).
Common mistakes
- Skipping the GCF check.
- Using numbers that multiply correctly but do not add correctly.
- Not verifying by expansion.
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