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.