# Let f(x) = 16x^{5} − 48x^{4} − 8x^{3} and g(x) = 8x^{2}. Find f of x over g of x.

**Solution:**

f(x) = 16x^{5} − 48x^{4} − 8x^{3}

g(x) = 8x^{2}

We know that

f(x)/ g(x) = (16x^{5} − 48x^{4} − 8x^{3})/ 8x^{2}

Taking out the common terms in the numerator

f(x)/ g(x) = [8x^{3} (2x^{2} - 6x - 1)]/ 8x^{2}

On further simplification

f(x)/ g(x) = x (2x^{2} - 6x - 1)

Using the multiplicative distributive property,

f(x)/ g(x) = x × 2x^{2} - x × 6x + x × (-1)

Removing the parentheses

f(x)/ g(x) = x × 2x^{2} - x × 6x - x

f(x)/ g(x) = 2x^{3} - 6x^{2} - x

Therefore, f(x)/ g(x) = 2x^{3} - 6x^{2} - x.

## Let f(x) = 16x^{5}− 48x^{4} − 8x^{3} and g(x) = 8x^{2}. Find f of x over g of x.

**Summary:**

Let f(x) = 16x^{5} − 48x^{4} − 8x^{3} and g(x) = 8x^{2} f of x over g of x is 2x^{3} - 6x^{2} - x.