Factoring Out the Common Factor
Factoring Out the Common Factor
Grade 7 Algebra — Turning sums into products!
1. What is Factoring?
Factoring means rewriting a mathematical expression (usually a polynomial) as a product of factors.
Think of it as the reverse of multiplication:
- Multiplication (forward): 3 × (2x + 3) = 6x + 9
- Factoring (backward): 6x + 9 = 3(2x + 3)
Key Idea: Factoring transforms a SUM into a PRODUCT.
2. What is a Common Factor?
A common factor is a factor that divides every term of a polynomial evenly.
Number Factor
12x + 18y
Both 12 and 18 are divisible by 6
Variable Factor
x³ + x²
Both terms contain x²
Combined Factor
6x² + 9x
Common factor is 3x