Reese Greene
07/24/2023 · Junior High School
uestion iven that \( f(x)=x^{2}+7 x+10 \) and \( g(x)=x+5 \), find \( (f+g)(x) \) and express the result a olynomial in simplest form.
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To find \( (f+g)(x) \), we need to add the functions \( f(x) \) and \( g(x) \).
Given:
\[
f(x) = x^2 + 7x + 10
\]
\[
g(x) = x + 5
\]
Now, we can compute \( (f+g)(x) \):
\[
(f+g)(x) = f(x) + g(x)
\]
\[
= (x^2 + 7x + 10) + (x + 5)
\]
Next, we combine like terms:
\[
= x^2 + 7x + x + 10 + 5
\]
\[
= x^2 + (7x + x) + (10 + 5)
\]
\[
= x^2 + 8x + 15
\]
Thus, the result is:
\[
(f+g)(x) = x^2 + 8x + 15
\]
This is the polynomial in simplest form.
Quick Answer
\( (f+g)(x) = x^2 + 8x + 15 \)
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