Question

In the following exercises, factor.

$3x^3-7x^2+6x-14$.

Short answer

The obtained factor for the expression $3x^3-7x^2+6x-14$ is,$\left(3x-7\right)\left(x^2+2\right)$.

Step-by-step solution

Given expression is,

$3x^3-7x^2+6x-14$.

The objective is, we need to find the factor for this expression.

First group the terms with the common factors.

$3x^3-7x^2+6x-14=\left(3x^3-7x^2\right)+\left(6x-14\right)$

Now factor out the common factors.

$$\begin{gathered} 3x^3-7x^2+6x-14=x^2\left(3x-7\right)+2\left(3x-7\right) \\ =\left(3x-7\right)\left(x^2+2\right) \end{gathered}$$

The obtained factors are,$\left(3x-7\right)\left(x^2+2\right)$

Step 3 Let us check the answer by multiplying the factors.

$$\begin{gathered} \left(3x-7\right)\left(x^2+2\right)=3x^3+6x-7x^2-14 \\ =3x^3-7x^2+6x-14 \end{gathered}$$

which is true.