Question

21. Given that f(x)= x^3– x² + 5x and g(x)= x^3 +5x^2 –2 determine
(g-f)(x)

Answer 1

(g - f)(x) = 6x² - 5x - 2

General Formulas and Concepts:

Pre-Algebra

• Distributive Property

Algebra I

• Combining Like Terms

Explanation:

Step 1: Define

f(x) = x³ - x² + 5x

g(x) = x³ + 5x² - 2

(g - f)(x) is g(x) - f(x)

Step 2: Evaluate

1. Substitute: (g - f)(x) = x³ + 5x² - 2 - (x³ - x² + 5x)
2. Distribute -1: (g - f)(x) = x³ + 5x² - 2 - x³ + x² - 5x
3. Combine like terms: (g - f)(x) = 6x² - 5x - 2