Answer:
x² - x + 1
Explanation:
Given:
r(x) = -x² + 3x
s(x) = 2x + 1
Required:
(s - r)(x)
Solution:
(s - r)(x) = s(x) - r(x)
Substitute
(s - r)(x) = (2x + 1) - (-x² + 3x)
Apply distribution property by multiply every term in the bracket by -1
(s - r)(x) = 2x + 1 + x² - 3x (recall: - × - = +; - × + = -)
Add like terms
(s - r)(x) = 2x - 3x + 1 + x²
(s - r)(x) = -x + 1 + x²
Rewrite in standard form
(s - r)(x) = x² - x + 1
