To solve for $f(x) + g(x)$ and express the result as a polynomial in simplest form, let's begin by defining the functions:

Given: $f(x) = x^2 + 2x - 63$ $g(x) = x - 7$

Now, we need to find $f(x) + g(x)$.

Step 1: Add the functions

$f(x) + g(x) = (x^2 + 2x - 63) + (x - 7)$

Step 2: Combine like terms

• The $x^2$ term has no counterpart in $g(x)$, so it remains $x^2$.
• Combine the $x$ terms: $2x + x = 3x$.
• Combine the constant terms: $-63 - 7 = -70$.

So, the sum is: $f(x) + g(x) = x^2 + 3x - 70$

Final Answer

The expression $f(x) + g(x)$ simplifies to: $\boxed{x^2 + 3x - 70}$

This is the polynomial in its simplest form.

Would you like any more details or have further questions?

Here are some related questions you might find interesting:

1. How do you find the product of two functions, like $f(x) \times g(x)$?
2. What are the roots of the polynomial $x^2 + 3x - 70$?
3. How do you complete the square for the polynomial $x^2 + 3x - 70$?
4. What is the derivative of the function $f(x) + g(x)$?
5. How do you find the inverse of a function like $g(x) = x - 7$?

Tip: When combining polynomials, always remember to group and simplify like terms for a cleaner expression.