Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i) `p(x)=2x^3+x^2-2x-1,g(x)=x+1`
(ii) `p(x)=x^3+3x^2+3x+1,g(x)=x+2`
(iii) `p(x)=x^3+4x^2+x+6,g(x)=x-3`

Explanation

To determine whether \( g(x) \) is a factor of \( p(x) \) using the Factor Theorem, we will follow these steps for each case:

### (i) \( p(x) = 2x^3 + x^2 - 2x - 1, g(x) = x + 1 \)

1. **Find the root of \( g(x) \)**:
\[ g(x) = x + 1 = 0 \implies x = -1 \]
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