We are asked to factor the quadratic expression $3x^2 + 11x - 4$ using the grouping method.

1. Problem Description

We are asked to factor the quadratic expression $3x^2 + 11x - 4$ using the grouping method.

2. Solution Steps

The grouping method involves rewriting the middle term ($11x$) as a sum of two terms, such that the product of their coefficients is equal to the product of the coefficients of the first and last terms. In this case, we want two numbers that multiply to $3 \cdot (-4) = -12$ and add up to $11$. These two numbers are $12$ and $-1$.

We can rewrite the middle term $11x$ as $12x - x$.

Then, we can rewrite the original expression as:

$3x^2 + 12x - x - 4$

Now we factor by grouping:

$3x(x + 4) - 1(x + 4)$

Finally, we factor out the common factor $(x + 4)$:

$(3x - 1)(x + 4)$

3. Final Answer

$(3x - 1)(x + 4)$