How do I find the value of f(x) over g(x) given f(x) = 16x^5 – 48x^4 – 8x^3 and g(x) = 8x^2?

Finding f(x) over g(x)

To find f(x) over g(x), we need to divide the polynomial function f(x) by g(x):

First, we define the functions:

f(x) = 16x5 - 48x4 - 8x3

g(x) = 8x2

Next, we perform the division:

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

We can simplify this by dividing 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

Combining these results gives:

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

Therefore, the value of f(x) over g(x) can be expressed as:

Final Result:

f(x) / g(x) = 2x³ – 6x² – x