https://file.aiquickdraw.com/mathbot/file/1729539846258w30ja26f.jpg

Let's examine the expression:

\[
3w^3 + 6w
\]

We need to factor out the greatest common factor (GCF).

### Step 1: Find the GCF of the coefficients
The coefficients are \(3\) and \(6\). The GCF of \(3\) and \(6\) is \(3\).

### Step 2: Find the GCF of the variable part
The variable terms are \(w^3\) and \(w\). The GCF of \(w^3\) and \(w\) is \(w\), since \(w\) is the lowest power of the variable common to both terms.

### Step 3: Factor the GCF
The GCF of the entire expression is \(3w\).

Now, factor out \(3w\) from the expression:

\[
3w^3 + 6w = 3w(w^2 + 2)
\]

So, the factored form is:

\[
\boxed{3w(w^2 + 2)}
\]

Would you like any further details or clarification on this?

### Related questions:
1. How do you factor out common terms in more complex polynomials?
2. What is the greatest common factor in terms of prime factorization?
3. How do you factor polynomials where no common factor exists?
4. Can you factor trinomials by grouping?
5. How do you check if a polynomial is factored completely?

**Tip:** Always check for both numerical and variable common factors when factoring an expression.

Factor out the greatest common factor. If the greatest common factor is 1, just retype the polynomial. 3w^3 + 6w

Learn how to factor the polynomial 3w^3 + 6w by identifying the greatest common factor (GCF). This detailed solution covers how to find the GCF of both coefficients and variable terms in algebraic expressions. Suitable for Grades 7-8 students.

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