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Let's break down the given information and solve the problem step by step.

We have the following functions:
1. \( F(x) = 2x^3 - 3x^2 + x - 6 \)
2. \( g(x) = x^2 - 4x + 5 \)
3. \( h(x) = x + 3 \)

The tasks are:
1. To find \( (F + g)(x) \), which is the sum of \( F(x) \) and \( g(x) \).
2. To find \( (g \times h)(x) \), which is the product of \( g(x) \) and \( h(x) \).

### a. \( (F + g)(x) \)
We add the functions \( F(x) \) and \( g(x) \):
\[
(F + g)(x) = F(x) + g(x)
\]
Substituting the given functions:
\[
(F + g)(x) = (2x^3 - 3x^2 + x - 6) + (x^2 - 4x + 5)
\]
Now combine like terms:
\[
(F + g)(x) = 2x^3 + (-3x^2 + x^2) + (x - 4x) + (-6 + 5)
\]
\[
(F + g)(x) = 2x^3 - 2x^2 - 3x - 1
\]

### b. \( (g \times h)(x) \)
We multiply the functions \( g(x) \) and \( h(x) \):
\[
(g \times h)(x) = g(x) \times h(x)
\]
Substituting the given functions:
\[
(g \times h)(x) = (x^2 - 4x + 5)(x + 3)
\]
Now apply the distributive property (FOIL method):
\[
(g \times h)(x) = x^2(x + 3) - 4x(x + 3) + 5(x + 3)
\]
Multiply each term:
\[
(g \times h)(x) = x^3 + 3x^2 - 4x^2 - 12x + 5x + 15
\]
Combine like terms:
\[
(g \times h)(x) = x^3 - x^2 - 7x + 15
\]

### Final Results:
1. \( (F + g)(x) = 2x^3 - 2x^2 - 3x - 1 \)
2. \( (g \times h)(x) = x^3 - x^2 - 7x + 15 \)

Would you like a more detailed explanation for any part of the solution?

Here are some related questions to explore:
1. How do you factor a cubic polynomial like \( x^3 - x^2 - 7x + 15 \)?
2. Can you solve \( F(x) = 0 \) for the roots of the cubic equation?
3. What is the domain and range of \( (F + g)(x) \)?
4. Can you graph the functions \( F(x) \), \( g(x) \), and \( h(x) \) together?
5. How does the product rule for derivatives apply to functions like \( g(x) \times h(x) \)?

**Tip:** When adding or multiplying polynomials, always combine like terms carefully to avoid mistakes.

Diketahui F(x) = 2x^3 - 3x^2 + x - 6, g(x) = x^2 - 4x + 5, h(x) = x + 3. Tentukan: a. (F + g)(x), b. (g × h)(x)

Learn how to solve the polynomial function addition and multiplication for F(x) = 2x^3 - 3x^2 + x - 6, g(x) = x^2 - 4x + 5, and h(x) = x + 3. Step-by-step solutions cover function addition (F + g)(x) and function multiplication (g × h)(x).

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