Detailed math worksheet for learning factoring using the greatest common factor (GCF), featuring definitions, step-by-step instructions, and practice problems.

Let’s solve the problem step by step.

We are given the expression:
6x² + 18x⁵

We need to factor out the GCF (Greatest Common Factor) using the 3 steps shown in the worksheet.

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STEP 1: Find the GCF of all terms

The two terms are:
- 6x²
- 18x⁵

First, find the GCF of the coefficients: 6 and 18.
Factors of 6: 1, 2, 3, 6
Factors of 18: 1, 2, 3, 6, 9, 18
→ The greatest common factor is 6

Now for the variables: x² and x⁵
When finding GCF of variables with exponents, take the variable with the smallest exponent.
So, GCF of x² and x⁵ is x²

Therefore, the overall GCF is: 6x²

✔ Step 1 Answer: GCF = 6x²

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STEP 2: Divide all terms by the GCF

Divide each term by 6x²:

First term: 6x² ÷ 6x² = 1
Second term: 18x⁵ 6x² = (18÷6) × (x⁵÷x²) = 3x³

✔ Step 2 Answer: Remainder inside parentheses will be (1 + 3x³)

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STEP 3: Put the GCF outside parenthesis and the remainder inside parenthesis

So we write:
6x²(1 + 3x³)

*Check by distributing:*
6x² × 1 = 6x²
6x² × 3x³ = 18x⁵
→ 6x² + 18x⁵ → matches original! ✔

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Final Answer:
6x²(1 + 3x³)