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### Question 16:
We are given the following:
- \( F(x) \) divided by \( (x - 3) \) gives a remainder of 5.
- \( F(x) \) divided by \( (x - 2) \) gives a remainder of 0.
- \( G(x) \) divided by \( (x - 3) \) gives a remainder of 2.
- \( G(x) \) divided by \( (x - 2) \) gives a remainder of -1.
- \( H(x) = 2F(x) - 3G(x) \).

We are asked to find the remainder of \( H(x) \) divided by \( (x - 2)(x - 3) \).

Let's proceed step by step:
1. From the division properties, we can substitute the given conditions:
   - \( F(3) = 5 \) and \( F(2) = 0 \)
   - \( G(3) = 2 \) and \( G(2) = -1 \)
2. Now, calculate \( H(3) \) and \( H(2) \):
   \[
   H(3) = 2F(3) - 3G(3) = 2(5) - 3(2) = 10 - 6 = 4
   \]
   \[
   H(2) = 2F(2) - 3G(2) = 2(0) - 3(-1) = 0 + 3 = 3
   \]
Thus, \( H(x) \) gives remainders of 4 when divided by \( (x - 3) \) and 3 when divided by \( (x - 2) \).

From the Chinese Remainder Theorem (or using Lagrange Interpolation), the remainder when \( H(x) \) is divided by \( (x - 2)(x - 3) \) is \( \boxed{4} \).

Answer: **E. \( x + 4 \)**.

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F(x) dibagi oleh (x - 3) dan (x - 2), sisanya berturut-turut 5 dan 0. G(x) dibagi oleh (x - 3) dan (x - 2), sisanya berturut-turut 2 dan -1. Diketahui H(x) = 2F(x) - 3G(x). Jika H(x) dibagi oleh (x - 2)(x - 3), maka sisa pembagiannya adalah ...

Explore how to solve a polynomial division problem using the Chinese Remainder Theorem. This question provides step-by-step calculations and applies algebraic concepts for dividing polynomials, determining remainders, and solving H(x) = 2F(x) - 3G(x). Suitable for advanced algebra students in Grades 11-12.

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