Given that f, of, x, equals, x, squared, plus, 2, x, minus, 63f(x)=x 
2
 +2x−63 and g, of, x, equals, x, minus, 7g(x)=x−7, find f, of, x, plus, g, of, xf(x)+g(x) and express the result as a polynomial in simplest form.

To find \( f(x) + g(x) \) and express it as a polynomial, we proceed step by step.

### Given:
1. \( f(x) = x^2 + 2x - 63 \)
2. \( g(x) = x - 7 \)

### Step 1: Add the functions together
We want to find \( f(x) + g(x) \):

\[
f(x) + g(x) = (x^2 + 2x - 63) + (x - 7)
\]

### Step 2: Combine like terms
Now, let's combine the terms of \( f(x) \) and \( g(x) \):

\[
f(x) + g(x) = x^2 + 2x + x - 63 - 7
\]
\[
f(x) + g(x) = x^2 + 3x - 70
\]

### Final Answer:
\[
f(x) + g(x) = x^2 + 3x - 70
\]

This is the polynomial in its simplest form.

Do you have any questions or would you like more details?

Here are 5 related questions to explore:
1. How do you find the difference between two functions?
2. What is the domain of \( f(x) + g(x) \)?
3. How would the graph of \( f(x) + g(x) \) look like?
4. What is the degree of the polynomial \( f(x) + g(x) \)?
5. How would \( f(x) - g(x) \) look in simplest form?

**Tip:** Always combine like terms carefully when adding or subtracting polynomials to avoid mistakes.

Given that f(x) = x^2 + 2x - 63 and g(x) = x - 7, find f(x) + g(x) and express the result as a polynomial in simplest form.

Explore how to add polynomials by simplifying the functions f(x) = x^2 + 2x - 63 and g(x) = x - 7 into a single polynomial in simplest form. This lesson covers key algebraic concepts and polynomial addition suitable for students in Grades 8-10.

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