Question

advanced algebra: concepts and connections
find the difference of functions s and r shown below.
r(x) = -x² + 3x
s(x) = 2x + 1
(s - r)(x) = (2x + 1) - (-x² + 3x)
complete
(s - r)(x) =
done
options:
-x² + x - 1
-x² + 5x - 1
x² + 5x + 1
x² - x + 1

Explanation:

Step1: Distribute the negative sign

We have \((s - r)(x)=(2x + 1)-(-x^{2}+3x)\). Distribute the negative sign to the terms inside the second parentheses: \(2x + 1+x^{2}-3x\).

Step2: Combine like terms

Combine the \(x\) - terms: \(2x-3x=-x\). So the expression becomes \(x^{2}-x + 1\).

Answer:

\(x^{2}-x + 1\) (corresponding to the option \(x^{2}-x + 1\))