Let f(x) = 16x⁵ − 48x⁴ − 8x³ and g(x) = 8x². Find f of x over g of x.

Solution:

f(x) = 16x⁵ − 48x⁴ − 8x³

g(x) = 8x²

We know that

f(x)/ g(x) = (16x⁵ − 48x⁴ − 8x³)/ 8x²

Taking out the common terms in the numerator

f(x)/ g(x) = [8x³ (2x² - 6x - 1)]/ 8x²

On further simplification

f(x)/ g(x) = x (2x² - 6x - 1)

Using the multiplicative distributive property,

f(x)/ g(x) = x × 2x² - x × 6x + x × (-1)

Removing the parentheses

f(x)/ g(x) = x × 2x² - x × 6x - x

f(x)/ g(x) = 2x³ - 6x² - x

Therefore, f(x)/ g(x) = 2x³ - 6x² - x.

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Let f(x) = 16x⁵− 48x⁴ − 8x³ and g(x) = 8x². Find f of x over g of x.

Summary:

Let f(x) = 16x⁵ − 48x⁴ − 8x³ and g(x) = 8x² f of x over g of x is 2x³ - 6x² - x.