Grade 7 Expressions: Factoring Expressions

Factor out GCF

What You'll Learn

Find GCF
Factor completely

📖Factoring

Factoring is distributing in reverse. Find the greatest common factor (GCF) of the terms, divide each term by it, and write it outside the parentheses: 12x + 18 = 6(2x + 3). When the first term is negative, factor out the negative GCF. Distribute to check.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
Factor: 10x − 18y = 2(?x − 9y)
1. Find the greatest common factor (GCF) of 10 and 18: it is 2.
2. Divide each term by 2: 10x ÷ 2 = 5x and −18y ÷ 2 = −9y.
3. So 10x − 18y = 2(5x − 9y).
4. Check by distributing: 2 × 5x = 10x and 2 × (−9y) = −18y.
5. Match 2(5x − 9y) to 2(?x − 9y): the missing number is 5.
Answer: 5
Example 2
Factor: 24k + 28 = 4(?k + 7)
1. Find the greatest common factor (GCF) of 24 and 28: it is 4.
2. Divide each term by 4: 24k ÷ 4 = 6k and 28 ÷ 4 = 7.
3. So 24k + 28 = 4(6k + 7).
4. Check by distributing: 4 × 6k = 24k and 4 × 7 = 28.
5. Match 4(6k + 7) to 4(?k + 7): the missing number is 6.
Answer: 6
Example 3
Factor: 6x − 12 = ?(x − 2)
1. Find the greatest common factor (GCF) of 6 and 12: it is 6.
2. Divide each term by 6: 6x ÷ 6 = x and −12 ÷ 6 = −2.
3. So 6x − 12 = 6(x − 2).
4. Check by distributing: 6 × x = 6x and 6 × (−2) = −12.
5. Match 6(x − 2) to ?(x − 2): the missing number is 6.
Answer: 6