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.

factor the trinomial 3x squared + 13x + 4

Discover how to factor the trinomial 3x^2 + 13x + 4 step by step. This solution covers algebraic concepts, including factoring by grouping, working with quadratic equations, and finding common binomial factors. Perfect for students in Grades 8-10.

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