To factor the quadratic expression $8x^2 + 12x$, we look for the greatest common factor (GCF) of the terms.

1. The GCF of $8x^2$ and $12x$ is $4x$.
2. Factoring $4x$ out of each term gives us:

$8x^2 + 12x = 4x(2x + 3)$

Thus, the correct factored form is:

$4x(2x + 3)$

Is there anything else you would like to understand about this problem?

Here are 5 more questions you might want to ask:

1. How do you factor more complex quadratic equations?
2. Can you explain how to find the GCF of two terms?
3. What are some common factoring techniques for polynomials?
4. How can you verify if your factored form is correct?
5. What are the steps to factor a trinomial?

Tip: Always check your factored form by multiplying the factors back together to ensure you get the original expression.