Question

given that $f(x) = x^2 - 8x + 15$ and $g(x) = x - 3$, find $f(x) + g(x)$ and express the result as a polynomial in simplest form.

Explanation:

Step1: Substitute the functions

We know that \( f(x) = x^2 - 8x + 15 \) and \( g(x)=x - 3 \). To find \( f(x)+g(x) \), we substitute the expressions of \( f(x) \) and \( g(x) \) into the sum:
\( f(x)+g(x)=(x^2 - 8x + 15)+(x - 3) \)

Step2: Combine like terms

First, remove the parentheses: \( x^2 - 8x + 15+x - 3 \)
Then, combine the like - terms for the \( x \) terms and the constant terms.
For the \( x \) terms: \( - 8x+x=-7x \)
For the constant terms: \( 15 - 3 = 12 \)
So, the simplified form is \( x^2-7x + 12 \)

Answer:

\( x^2-7x + 12 \)