Question

is (x-3) a factor of (x³ - 3x² + 2x + 2)? yes no

Explanation:

Step1: Apply Factor Theorem

If $(x-3)$ is a factor, then $f(3)=0$, where $f(x)=x^3 - 3x^2 + 2x + 2$.

Step2: Calculate $f(3)$

$$\begin{align*} f(3)&=3^3 - 3(3)^2 + 2(3) + 2\\ &=27 - 27 + 6 + 2\\ &=8 \end{align*}$$

Step3: Evaluate result

Since $f(3)=8
eq0$, $(x-3)$ is not a factor.

Answer:

No