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To find the quotient when \( P(x) = 3x^2 - 5x + 1 \) is divided by \( (3x + 1) \), we can use polynomial division.

Let's go through the steps:

### Step-by-Step Solution
1. **Divide the leading term:** Take the leading term of the polynomial, \( 3x^2 \), and divide it by the leading term of the divisor, \( 3x \):
   \[
   \frac{3x^2}{3x} = x
   \]
   So, the first term of the quotient is \( x \).

2. **Multiply and Subtract:** Multiply \( x \) by \( 3x + 1 \):
   \[
   x \cdot (3x + 1) = 3x^2 + x
   \]
   Now, subtract this result from \( P(x) \):
   \[
   (3x^2 - 5x + 1) - (3x^2 + x) = -6x + 1
   \]

3. **Repeat the Division:** Now, divide the new leading term \( -6x \) by \( 3x \):
   \[
   \frac{-6x}{3x} = -2
   \]
   So, the next term in the quotient is \( -2 \).

4. **Multiply and Subtract Again:** Multiply \( -2 \) by \( 3x + 1 \):
   \[
   -2 \cdot (3x + 1) = -6x - 2
   \]
   Subtract this from \( -6x + 1 \):
   \[
   (-6x + 1) - (-6x - 2) = 3
   \]

### Result
The remainder is \( 3 \), so we can write:
\[
P(x) = (3x + 1)(x - 2) + 3
\]
Thus, the quotient is \( x - 2 \) with a remainder of \( 3 \), which can be expressed as:
\[
x - 2 + \frac{3}{3x + 1}
\]

### Answer
The correct answer is:
\[
\boxed{x - 2 + \frac{3}{3x + 1}}
\]

This matches the answer choice:
- **"3x - 6 + 3/(3x + 1)"**

What is the quotient when P(x) = 3x^2 - 5x + 1 is divided by (3x + 1)?

Solve the division of the polynomial P(x) = 3x^2 - 5x + 1 by (3x + 1) using polynomial division. This solution demonstrates key algebraic steps for dividing polynomials, ideal for high school students.

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