General Factoring and Its Application
5-12Solving Equations by Factoring
Overview
Zero-Product Property: if AB = 0, then A = 0 or B = 0. Set polynomial = 0, factor, solve each factor.
Key ideas
- Move all terms to one side; the other side is 0.
- Factor completely.
- Set each factor equal to 0 and solve.
Worked examples
Example 1
Problem. Solve x^2 − 5x + 6 = 0.
Solution. (x − 2)(x − 3) = 0 → x = 2 or 3.
Example 2
Problem. Solve x^2 = 9.
Solution. x^2 − 9 = 0 → (x − 3)(x + 3) = 0 → x = ±3.
Practice
Try each one. Click Show answer when ready.
- 1.
Solve x^2 + x − 12 = 0.
- 2.
Solve x^2 − 6x + 8 = 0.
- 3.
Solve x^2 = 16.
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Solve by factoring: x² − 5x + 6 = 0.
- 2.
Solve by factoring: 2x² + x − 3 = 0.