factor out the greatest common factor: 3x^2/2 + 9x/2

To factor out the greatest common factor (GCF) from the expression:

\[
\frac{3x^2}{2} + \frac{9x}{2}
\]

### Step 1: Identify the GCF of the terms.
- The terms are \(\frac{3x^2}{2}\) and \(\frac{9x}{2}\).
- The GCF of the numerical coefficients 3 and 9 is 3.
- Both terms have a factor of \(x\), so the GCF of the variables is \(x\).
  
Thus, the GCF of the entire expression is \(\frac{3x}{2}\).

### Step 2: Factor out the GCF.

Factor \(\frac{3x}{2}\) from both terms:

\[
\frac{3x^2}{2} + \frac{9x}{2} = \frac{3x}{2}(x + 3)
\]

So, the factored form is:

\[
\frac{3x}{2}(x + 3)
\]

Would you like any further details or explanations?

Here are 5 related questions for you to explore:
1. How do you factor an expression with different denominators?
2. How do you find the GCF of multiple terms with variables?
3. What is factoring by grouping, and how is it different from GCF factoring?
4. How do you apply the distributive property when factoring expressions?
5. Can factoring help in solving quadratic equations?

**Tip:** Always start by factoring out the GCF in an expression to simplify it before attempting other methods.

Factor out the greatest common factor: 3x^2/2 + 9x/2

Learn how to factor out the greatest common factor (GCF) from the expression 3x^2/2 + 9x/2. This step-by-step solution walks through identifying the GCF and factoring it out, covering core algebraic concepts. Suitable for students in Grades 7-9.

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