Show that `(x-2)` is a factor of the polynomial `f(x)=2x^3-3x^2-17 x+30` and hence factorize `f(x)dot`

Explanation

To show that \( (x - 2) \) is a factor of the polynomial \( f(x) = 2x^3 - 3x^2 - 17x + 30 \) and to factorize \( f(x) \), we will follow these steps:

### Step 1: Verify if \( (x - 2) \) is a factor
To determine if \( (x - 2) \) is a factor of \( f(x) \), we will evaluate \( f(2) \). If \( f(2) = 0 \), then \( (x - 2) \) is a factor.

**Calculation:**
\[
f(2) = 2(2)^3 - 3(2)^2 - 17(2) + 30
...