13. Given f(x) = x ^ 2 + 2x - 8 and g(x) = 6x ^ 2 - 10x + 3 what is (f + g)(x)

A. 6x ^ 2 - 12x - 5

C. 7x ^ 2 - 8x - 11

B. 7x ^ 2 - 12x - 5

D. 7x ^ 2 - 8x - 5

14. Given f(x) = 6x + 4 and g(x) = 2x - 7 what is (fg) (x)^ *

A. 8x - 3

C. 4x + 11

B. 12x ^ 2 - 28

D. 12x ^ 2 - 34x - 28

Let's solve both problems step by step.

### Problem 13:
Given:
- \( f(x) = x^2 + 2x - 8 \)
- \( g(x) = 6x^2 - 10x + 3 \)

We need to find \((f + g)(x)\).

\[
(f + g)(x) = f(x) + g(x)
\]

Substituting the given functions:

\[
(f + g)(x) = (x^2 + 2x - 8) + (6x^2 - 10x + 3)
\]

Now, combine like terms:

\[
= x^2 + 6x^2 + 2x - 10x - 8 + 3
\]

Simplifying:

\[
= 7x^2 - 8x - 5
\]

So, the correct answer is **D. 7x^2 - 8x - 5**.

### Problem 14:
Given:
- \( f(x) = 6x + 4 \)
- \( g(x) = 2x - 7 \)

We need to find \((fg)(x)\), which means multiplying \(f(x)\) and \(g(x)\):

\[
(fg)(x) = f(x) \cdot g(x)
\]

Substitute the given functions:

\[
(fg)(x) = (6x + 4)(2x - 7)
\]

Use the distributive property (FOIL method) to expand:

\[
(fg)(x) = 6x \cdot 2x + 6x \cdot (-7) + 4 \cdot 2x + 4 \cdot (-7)
\]

Simplifying:

\[
= 12x^2 - 42x + 8x - 28
\]

Combine like terms:

\[
= 12x^2 - 34x - 28
\]

So, the correct answer is **D. 12x^2 - 34x - 28**.

---

Would you like further details or explanations on any of the steps? Here are some related questions:

1. How do you combine like terms when adding polynomials?
2. What is the FOIL method in algebra?
3. How do you determine the degree of a polynomial?
4. What are the steps to factor a quadratic equation?
5. How do you identify the coefficients in a polynomial equation?

**Tip:** Always double-check your signs when combining like terms to avoid errors in your final answer.

13. Given f(x) = x^2 + 2x - 8 and g(x) = 6x^2 - 10x + 3 what is (f + g)(x)?
A. 6x^2 - 12x - 5
B. 7x^2 - 12x - 5
C. 7x^2 - 8x - 11
D. 7x^2 - 8x - 5

14. Given f(x) = 6x + 4 and g(x) = 2x - 7 what is (fg)(x)?
A. 8x - 3
B. 12x^2 - 28
C. 4x + 11
D. 12x^2 - 34x - 28

Learn how to solve polynomial addition and multiplication problems such as (f + g)(x) = x^2 + 2x - 8 + 6x^2 - 10x + 3 and (fg)(x) = (6x + 4)(2x - 7). This guide provides a step-by-step solution, covering essential algebraic concepts and suitable for students in Grades 9-10.

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