What is the factored form of 8*x*2 + 12*x*?

4(4*x*2 + 8*x*)  

4*x*(2*x* + 3)  

8*x*(*x* + 4)

8*x*(*x2* + 4)

To find the factored form of the expression \(8x^2 + 12x\), we can follow these steps:

1. **Find the greatest common factor (GCF):**  
   The GCF of \(8x^2\) and \(12x\) is \(4x\), because:
   - The GCF of 8 and 12 is 4.
   - Both terms have at least one factor of \(x\).

2. **Factor out the GCF:**  
   We factor out \(4x\) from each term in the expression:
   \[
   8x^2 + 12x = 4x(2x + 3)
   \]

Therefore, the factored form of \(8x^2 + 12x\) is:

\[
\boxed{4x(2x + 3)}
\]

Among the given options, this matches option **2**: \(4x(2x + 3)\).

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Would you like further details or have any questions about this factorization process?

Here are five related questions to expand your understanding:

1. How do you find the greatest common factor (GCF) of two terms?
2. What is the factored form of \(15x^2 + 25x\)?
3. Can you explain why \(8x(x + 4)\) is not the correct factorization for \(8x^2 + 12x\)?
4. How can we check if our factorization is correct?
5. What happens if an expression has no common factors other than 1?

**Tip:** Always start by finding the greatest common factor (GCF) when factoring expressions. This will simplify the process and help ensure you get the correct factors.

Learn how to factor the expression 8x^2 + 12x step-by-step with a detailed explanation. Understand the concept of factoring polynomials and finding the greatest common factor (GCF). Suitable for students in Grades 7-9.

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