To factor the expression \(3x(x + 2) + 4(x + 2)\) completely, we can follow these steps:

1. **Identify and factor out the common factor** in both terms.

We see that \((x + 2)\) is a common factor in both terms of the expression.

2. **Factor out the common factor \((x + 2)\)** from the expression:

\[
3x(x + 2) + 4(x + 2) = (x + 2)(3x) + (x + 2)(4)
\]

Using the distributive property, we can combine the two terms:

\[
(x + 2)(3x) + (x + 2)(4) = (x + 2)(3x + 4)
\]

So, the completely factored form of \(3x(x + 2) + 4(x + 2)\) is:

\[
(x + 2)(3x + 4)
\]

Would you like any further details or have any questions?

Here are 8 related questions that you might find useful:
1. How do you identify common factors in polynomial expressions?
2. What is the distributive property and how is it used in factoring?
3. Can you provide an example of factoring an expression with different common factors?
4. How do you factor quadratic expressions?
5. What are the steps to factor polynomials by grouping?
6. How do you check if a factored form is correct?
7. What are some common factoring techniques for higher-degree polynomials?
8. How can you use factoring to solve polynomial equations?

**Tip:** Always look for common factors in each term of a polynomial expression as the first step in the factoring process. This can simplify the expression significantly and make further factoring easier.

Learn how to factor completely the expression 3x(x + 2) + 4(x + 2) with a detailed step-by-step solution. This problem covers key concepts in algebra, including factoring polynomial expressions and the distributive property. Suitable for high school students (Grades 9-12).

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