How to Factor Trinomials (x² + bx + c)
Factor x² + bx + c in two steps with two worked examples and the sign mistake to avoid.
The method
- x² + bx + c = (x + p)(x + q)
- p · q = c and p + q = b
Find two numbers that multiply to c and add to b.
Example 1
Factor x² + 7x + 12
- Pairs that multiply to 12: 3 and 4
- 3 + 4 = 7 ✓
- (x + 3)(x + 4)
(x + 3)(x + 4)
Example 2
Factor x² − 2x − 15
- Multiply to −15, add to −2
- −5 and 3 work
- (x − 5)(x + 3)
(x − 5)(x + 3)
Common mistake
x² − 2x − 15 = (x + 5)(x − 3)
Check the signs: the two numbers must add to b, not just multiply to c.
Multiply your answer back out to check it.
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