Let's factor the expression $3x^2 + 6x + 4x + 8$.

First, we can combine the like terms:

$3x^2 + (6x + 4x) + 8 = 3x^2 + 10x + 8$

Next, we'll look for factors by grouping. We can group the terms as follows:

$(3x^2 + 6x) + (4x + 8)$

Now, factor out the common factors from each group:

$3x(x + 2) + 4(x + 2)$

Notice that both groups contain a common factor of $(x + 2)$. We can factor this out:

$(3x + 4)(x + 2)$

So, the factored form of $3x^2 + 10x + 8$ is:

$(3x + 4)(x + 2)$

Would you like more details, or do you have any questions?

Here are five related questions you might be interested in:

1. How can you factor a quadratic expression using the quadratic formula?
2. What are the steps to factor a trinomial when the leading coefficient is not 1?
3. How do you factor by grouping with more than four terms?
4. How can factoring help solve quadratic equations?
5. What is the difference between factoring and expanding an expression?

Tip: Always check for common factors across all terms before starting to factor by grouping.