Which of the following is the factor of the equation $7x^3-3x^2+2x-6$?

Let's examine all the options given above.

• When $(x-1)$ i.e. $x=1$

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

Let's replace x with $1$.

$$\begin{gathered} 7{\left(1\right)}^3-3{\left(1\right)}^2+2\left(1\right)-6 \\ = 7-3+2-6 \\ = 4+2-6 \\ =6-6 \\ =0 \end{gathered}$$

Therefore it is the correct answer.

• When $(x+1)$ i.e. $x=-1$

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

Let's replace x with $-1$.

$$\begin{gathered} =7{(-1)}^3-3{(-1)}^2+2(-1)-6 \\ =-7-3-2-6 \\ = -10-2-6 \\ = -12-6 \\ = -18 \end{gathered}$$

Therefore it is not the correct answer.

• When $(x+2)$ i.e. $x=-2$

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

Let's replace x with $-2$.

$$\begin{gathered} =7{(-2)}^3-3{(-2)}^2+2(-2)-6 \\ = -56-12-4-6 \\ = -68-4-6 \\ = -72-6 \\ = -78 \end{gathered}$$

Therefore it is not the correct answer.