Show that
(i) `x+3 ` is factor of `69+11x-x^(2)+x^(3)`
(ii) `2x-3` is factor of `x+2x^(3)-9x^(2)+12`

Explanation

To show that \( x + 3 \) is a factor of \( 69 + 11x - x^2 + x^3 \) and \( 2x - 3 \) is a factor of \( x + 2x^3 - 9x^2 + 12 \), we will use the Factor Theorem. According to the Factor Theorem, a polynomial \( f(x) \) has a factor \( (x - c) \) if and only if \( f(c) = 0 \).

### Part (i): Show that \( x + 3 \) is a factor of \( 69 + 11x - x^2 + x^3 \)

1. **Identify the polynomial**: Let \( p(x) = 69 + 11x - x^2 + x^3 \).
2. **Set \( g(x) = x + 3 \)**: To use the Factor Theorem, we need to find \( c \) such that \( g(c) = 0 \). Here, \( g(x) = 0 \) gives us \( x + 3 = 0 \) or \( x = -3 \).
3. **Evaluate \( p(-3) \)**:
\[
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