Factoring Quadratics
Finding Factor Pairs for Quadratics
For a quadratic in the form x² + bx + c, the key step is finding two numbers whose product is c and whose sum is b.
The multiply-and-add rule
The same two numbers must satisfy both conditions. A factor pair may multiply to the constant correctly but still be wrong if it does not add to the middle coefficient.
How to find the right pair
- List the factor pairs of the constant c.
- Add each pair.
- Choose the pair whose sum equals b.
- Check signs before writing the brackets.
Worked example
Factor x² + 9x + 20
- Factor pairs of 20 include 1 and 20, 2 and 10, and 4 and 5.
- 4 × 5 = 20.
- 4 + 5 = 9.
x² + 9x + 20 = (x + 4)(x + 5).
Common mistakes
- Choosing the first pair that multiplies correctly.
- Adding incorrectly when one or both numbers are negative.
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