1. **Problem Statement:** Find the remainder when the polynomial $p(x)$ is divided by $3x + 1$. 2. **Recall the Remainder Theorem:** When a polynomial $f(x)$ is divided by a linear divisor of the form $ax + b$, the remainder is $f\left(-\frac{b}{a}\right)$. 3. **Apply the theorem:** Here, the divisor is $3x + 1$, so $a = 3$ and $b = 1$. The remainder is given by evaluating $p\left(-\frac{1}{3}\right)$. 4. **Evaluate the remainder:** Substitute $x = -\frac{1}{3}$ into $p(x)$ to find the remainder. 5. **Final answer:** The remainder when $p(x)$ is divided by $3x + 1$ is $p\left(-\frac{1}{3}\right)$. Note: Since the explicit form of $p(x)$ is not provided, the remainder is expressed in terms of $p\left(-\frac{1}{3}\right)$.