To factor the expression \( 3x^2 + 6x + 4x + 8 \), we can proceed by grouping the terms.

1. Group the terms in pairs:
   \[
   (3x^2 + 6x) + (4x + 8)
   \]

2. Factor out the common factor from each group:
   - From \( 3x^2 + 6x \), factor out \( 3x \):
     \[
     3x(x + 2)
     \]
   - From \( 4x + 8 \), factor out \( 4 \):
     \[
     4(x + 2)
     \]

3. Now, notice that \( x + 2 \) is a common factor:
   \[
   3x(x + 2) + 4(x + 2)
   \]
   This can be factored as:
   \[
   (3x + 4)(x + 2)
   \]

So, the factored form of \( 3x^2 + 6x + 4x + 8 \) is \( \boxed{(3x + 4)(x + 2)} \).

Would you like further details or have any questions? 

Here are five related questions for further practice:

1. Factor the expression \( 2x^2 + 8x + 3x + 12 \).
2. Factor \( 5x^2 + 15x + 2x + 6 \).
3. Factor the quadratic expression \( 4x^2 + 16x + 4x + 16 \).
4. What is the factored form of \( 7x^2 + 21x + 14x + 42 \)?
5. Factor \( x^2 + 5x + 6 \).

**Tip:** When factoring by grouping, always look for common factors within each group first, and then check if there's a common binomial factor to factor out.

Learn how to factor the expression 3x^2 + 6x + 4x + 8 step-by-step with detailed explanations. This problem covers key algebraic concepts including factoring by grouping and the quadratic equation formula. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation