Answer: x⁵ - 2x³ + 2x² - 8x + 4
Step-by-step explanation:
f(x) = x³ - 4x + 2
g(x) = x² + 2
(f · g)(x) = (x² + 2) (x³ - 4x + 2)
= x²(x³ - 4x + 2) + 2(x³ - 4x + 2)
= x⁵ - 4x³ + 2x² + 2x³ - 8x + 4
= x⁵ - 2x³ + 2x² - 8x + 4 ⇒ added like terms (-4x³ and 2x³)
