Section 7.4: Factoring Basics
Factoring is the process of writing a polynomial as a product of its factors. Start with the greatest common factor (GCF) first, then proceed with factoring by grouping or special patterns.
Example 1
Factor: \( 6x^2 + 9x \)
Step 1: Identify the GCF: \( 3x \)
Step 2: Factor out \( 3x \): \( 3x(2x + 3) \)
Example 2
Factor: \( x^2 + 5x + 6 \)
Step 1: Find two numbers that multiply to 6 and add to 5: 2 and 3
Step 2: Factor: \( (x + 2)(x + 3) \)
Practice Problems
- Factor: \( 8x^3 + 12x^2 \)
- Factor: \( x^2 + 7x + 12 \)
- Factor: \( 15y^2 - 25y \)
- Factor: \( x^2 - 9 \)
- Factor: \( 6a^2 + 11a + 3 \)