Factoring Patterns
5-7Factoring Pattern for x² + bx + c, c positive
Overview
Find two numbers that multiply to c and add to b. Both numbers share the sign of b.
Key ideas
- List factor pairs of c.
- Pick the pair that sums to b.
- Both signs are positive if b > 0, negative if b < 0.
Worked examples
Example 1
Problem. Factor x^2 + 7x + 12.
Solution. (x + 3)(x + 4) (3·4 = 12, 3 + 4 = 7)
Example 2
Problem. Factor x^2 − 5x + 6.
Solution. (x − 2)(x − 3)
Practice
Try each one. Click Show answer when ready.
- 1.
Factor x^2 + 8x + 15.
- 2.
Factor x^2 − 9x + 20.
- 3.
Factor x^2 + 10x + 24.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Factor: x² + 9x + 20.
- 2.
Factor: x² + 11x + 24.