Section 1.4: Factoring & Quadratics Review
This section reviews factoring techniques and quadratic equations, including factoring trinomials, difference of squares, and solving quadratics by factoring.
Example 1: Factoring a Trinomial
Factor \( x^2 + 5x + 6 \).
Step 1: Find two numbers that multiply to 6 and add to 5 → 2 and 3
Step 2: Factor: \( x^2 + 5x + 6 = (x + 2)(x + 3) \)
Example 2: Solving a Quadratic Equation by Factoring
Solve \( x^2 - 7x + 10 = 0 \).
Step 1: Factor: \( x^2 - 7x + 10 = (x - 5)(x - 2) \)
Step 2: Set each factor to 0 → \( x - 5 = 0 \) or \( x - 2 = 0 \)
Solution: \( x = 5, 2 \)
Practice Problems
- Factor \( x^2 + 9x + 20 \)
- Factor \( x^2 - 16 \)
- Solve \( x^2 + 4x - 12 = 0 \) by factoring
- Factor \( 2x^2 + 7x + 3 \)
- Solve \( x^2 - 6x + 8 = 0 \) by factoring