The problem asks to factor the quadratic expression $3x^2 + 2x - 1$.

1. Problem Description

The problem asks to factor the quadratic expression $3x^2 + 2x - 1$.

2. Solution Steps

To factor the quadratic expression $3x^2 + 2x - 1$, we look for two numbers that multiply to $3 \cdot (-1) = -3$ and add up to $2$. These two numbers are $3$ and $-1$. We can rewrite the middle term using these two numbers:

$3x^2 + 2x - 1 = 3x^2 + 3x - x - 1$.

Now, we can factor by grouping:

$3x^2 + 3x - x - 1 = 3x(x + 1) - 1(x + 1)$.

We can factor out the common term $(x + 1)$:

$3x(x + 1) - 1(x + 1) = (3x - 1)(x + 1)$.

Therefore, $3x^2 + 2x - 1 = (3x - 1)(x + 1)$.

3. Final Answer

$(3x-1)(x+1)$