Which of the following is the factor of the equation $x^3-4x^2+5x-2$?

Let's examine all the options given above.

• When $(x-1)$ i.e. $x=1$

$x^3-4x^2+5x-2$

Let's replace x with $1$.

$$\begin{gathered} {\left(1\right)}^3-4{\left(1\right)}^2+5\left(1\right)-2 \\ = 1-4+5-2 \\ = -3+5-2 \\ =2-2 \\ =0 \end{gathered}$$

Therefore it is the correct answer.

• When $(x+1)$ i.e. $x=-1$

$x^3-4x^2+5x-2$

Let's replace x with $-1$.

$$\begin{gathered} ={(-1)}^3-4{(-1)}^2+5(-1)-2 \\ =-1-4-5-2 \\ = -5-5-2 \\ = -10-2 \\ = -12 \end{gathered}$$

Therefore it is not the correct answer.

• When $(x-2)$ i.e. $x=2$

$x^3-4x^2+5x-2$

Let's replace x with $2$.

$$\begin{gathered} ={\left(2\right)}^3-4{\left(2\right)}^2+5\left(2\right)-2 \\ = 8-16+10-2 \\ = -8+10-2 \\ = 2-2 \\ = 0 \end{gathered}$$

Therefore it is the correct answer.