Question

Given that f, of, x, equals, x, squared, minus, 3, x, minus, 10f(x)=x
2
−3x−10 and g, of, x, equals, x, plus, 2g(x)=x+2, find left parenthesis, f, plus, g, right parenthesis, left parenthesis, x, right parenthesis(f+g)(x) and express the result as a polynomial in simplest form.

Answer 1

To find \( (f + g)(x) \), we need to add the functions \( f(x) \) and \( g(x) \) together.

Given:
- \( f(x) = x^2 - 3x - 10 \)
- \( g(x) = x + 2 \)

Now we will add these two functions:

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

Substituting the expressions we have for \( f(x) \) and \( g(x) \):

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

Now we'll combine like terms:

1. The \( x^2 \) term is \( x^2 \).
2. The linear \( x \) terms are \( -3x + x = -2x \).
3. The constant terms are \( -10 + 2 = -8 \).

Putting it all together, we have:

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

Thus, the result expressed as a polynomial in simplest form is:

\[
\boxed{x^2 - 2x - 8}
\]