Question

or completely.
$3x^2 + x - 4$

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 \(4\times(-3)=-12\) and \(4 + (-3)=1\).

Step2: Rewrite the middle term

Rewrite the middle term \(x\) 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

Now, factor out the common binomial \((3x + 4)\):
\((3x + 4)(x - 1)\)

Answer:

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