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 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.

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.

Learn how to simplify the polynomial expression f(x) + g(x) for the functions f(x) = x^2 + 2x - 63 and g(x) = x - 7. This step-by-step solution breaks down the process of combining like terms in polynomial addition. Suitable for students in Grades 8-10.

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