Question

factor.
$3x^2 - 19x - 14$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times(-14)= -42\) and add up to \(-19\). The numbers are \(-21\) and \(2\) since \(-21\times2 = -42\) and \(-21 + 2=-19\).

Step2: Rewrite the middle term

Rewrite \(-19x\) as \(-21x+2x\) in the quadratic expression:
\(3x^{2}-21x + 2x-14\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((3x^{2}-21x)+(2x - 14)\)
Factor out the greatest common factor from each group:
\(3x(x - 7)+2(x - 7)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x - 7)\):
\((3x + 2)(x - 7)\)

Answer:

\((3x + 2)(x - 7)\)