How do you find f(x) over g(x) for the functions f(x) = 16x^5 – 48x^4 – 8x^3 and g(x) = 8x^2?

To find f(x) over g(x), we need to set up the fraction of the two functions:

Given:

• f(x) = 16x⁵ – 48x⁴ – 8x³
• g(x) = 8x²

We express this as:

f(x) / g(x) = (16x⁵ – 48x⁴ – 8x³) / (8x²)

Now, we can simplify the fraction:

The first step is to divide each term in the numerator by the denominator:

= 16x⁵ / 8x² – 48x⁴ / 8x² – 8x³ / 8x²

Calculating each term:

• 16x⁵ / 8x² = 2x³
• -48x⁴ / 8x² = -6x²
• -8x³ / 8x² = -x

Putting it all together, we have:

f(x) / g(x) = 2x³ – 6x² – x

This expression simplifies our functions and gives us the required ratio of f(x) over g(x). You can now use this result for further analysis or calculations as needed.