Factoring Out the GCF Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Factor 6x2+9x6x^2 + 9x.

Solution

  1. 1
    Step 1: Find the GCF of 6x26x^2 and 9x9x: GCF of 6 and 9 is 3; both have at least xx. GCF = 3x3x.
  2. 2
    Step 2: Divide each term: 6x2÷3x=2x6x^2 \div 3x = 2x and 9x÷3x=39x \div 3x = 3.
  3. 3
    Step 3: Write as product: 3x(2x+3)3x(2x + 3).
  4. 4
    Check: 3x(2x+3)=6x2+9x3x(2x + 3) = 6x^2 + 9x ✓

Answer

3x(2x+3)3x(2x + 3)
Factoring out the GCF is the reverse of distribution. Find the largest factor common to every term, divide each term by it, and write the result as a product.

About Factoring Out the GCF

Factoring out the greatest common factor (GCF) means identifying the largest expression that divides every term, then rewriting the polynomial as that GCF times what remains.

Learn more about Factoring Out the GCF →

More Factoring Out the GCF Examples

Example 2 medium

Factor [formula].

Example 3 easy

Factor [formula].

Example 4 hard

Factor [formula].

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