Factor completely. 3, x, squared, minus, x, minus, 4 3x 2 −x−4

Problem: Factor the quadratic expression $3x^2 - x - 4$.

Steps

1. Identify coefficients for the AC method
   Find two numbers that multiply to $a \cdot c = 3 \cdot (-4) = -12$ and add to $b = -1$. The numbers are $-4$ and $3$.
   $$3x^2 - 4x + 3x - 4$$
2. Factor by grouping
   Group the first two terms and the last two terms: $(3x^2 - 4x) + (3x - 4)$.
   $$x(3x - 4) + 1(3x - 4)$$
3. Factor out the common binomial
   Factor out $(3x - 4)$ from the expression.
   $$(3x - 4)(x + 1)$$