To factor the trinomial $3x^2 + 13x + 4$, we follow these steps:

1. Multiply the leading coefficient (3) by the constant term (4): $3 \times 4 = 12$

2. Find two numbers that multiply to 12 and add to 13 (the middle coefficient): $12 \times 1 = 12 \quad \text{and} \quad 12 + 1 = 13$ So, the two numbers are 12 and 1.

3. Rewrite the middle term $13x$ as $12x + x$: $3x^2 + 12x + x + 4$

4. Group the terms in pairs: $(3x^2 + 12x) + (x + 4)$

5. Factor out the greatest common factor (GCF) from each group: $3x(x + 4) + 1(x + 4)$

6. Factor out the common binomial factor $(x + 4)$: $(3x + 1)(x + 4)$

Thus, the factored form of the trinomial $3x^2 + 13x + 4$ is: $(3x + 1)(x + 4)$

Would you like further details or have any questions?

Here are 5 related questions for further practice:

1. Factor the trinomial $2x^2 + 7x + 3$.
2. Factor $4x^2 + 12x + 9$.
3. Solve $3x^2 + 13x + 4 = 0$ using factoring.
4. How do you factor $x^2 + 5x + 6$?
5. What happens if you cannot factor a trinomial easily?

Tip: When factoring trinomials, always check for a greatest common factor (GCF) before starting.