Question

question
factor completely.
$3x^2 - x - 2$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(3\times(-2)= -6\) and add up to \(-1\). The numbers are \(-3\) and \(2\) since \(-3\times2 = -6\) and \(-3 + 2=-1\).

Step2: Rewrite the middle term

Rewrite the middle term \(-x\) using \(-3x\) and \(2x\):
\(3x^{2}-3x + 2x-2\)

Step3: Group and factor

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

Step4: Factor out the common binomial

Now, factor out the common binomial \((x - 1)\):
\((3x + 2)(x - 1)\)

Answer:

\((3x + 2)(x - 1)\)