Question

question
factor completely.
$3x^2 - x - 4$
answer attempt 1 out of 2
$(x + 6) \cdot (3x + 5)$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times(-4)= -12\) and add up to \(-1\). The numbers are \(-4\) and \(3\) since \(-4\times3 = -12\) and \(-4 + 3=-1\).

Step2: Rewrite the middle term

Rewrite \(-x\) as \(-4x + 3x\) in the quadratic expression:
\(3x^{2}-4x + 3x-4\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((3x^{2}-4x)+(3x - 4)\)
Factor out the greatest common factor from each group:
\(x(3x - 4)+1(3x - 4)\)

Step4: Factor out the common binomial

Factor out \((3x - 4)\) from both terms:
\((3x - 4)(x + 1)\)

Answer:

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