Check whether the polynomial `f(x)=x^(2)-3` is a factor of the polynomial `g(x)` where `g(x)=2x^(4)+3x^(3)-2x^(2)-9x-12`.

Explanation

To check whether the polynomial \( f(x) = x^2 - 3 \) is a factor of the polynomial \( g(x) = 2x^4 + 3x^3 - 2x^2 - 9x - 12 \), we can use the Factor Theorem. According to the Factor Theorem, if \( f(x) \) is a factor of \( g(x) \), then \( g(r) = 0 \) for every root \( r \) of \( f(x) \).

### Step 1: Find the roots of \( f(x) \)

The polynomial \( f(x) = x^2 - 3 \) can be factored as:

\[ f(x) = 0 \implies x^2 - 3 = 0 \implies x^2 = 3 \implies x = \sqrt{3} \text{ or } x = -\sqrt{3} \]