Question

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

Answer 1

Answer:

$2x^3-6x^2-x$

Step-by-step explanation:

$\frac{f(x)}{g(x)}=\frac{16x^5-48x^4-8x^3}{8x^2}$

$\frac{f(x)}{g(x)}=\frac{16x^5}{8x^2}-\frac{48x^4}{8x^2}-\frac{8x^3}{8x^2}$

$\frac{f(x)}{g(x)}=\frac{16}{8}x^{5-2}-\frac{48}{8}x^{4-2}-\frac{8}{8}x^{3-2}$

$\frac{f(x)}{g(x)}=2x^{3}-6x^2-1x^1$

$\frac{f(x)}{g(x)}=2x^3-6x^2-x$

Answer 2

Answer:

First, we have to express the fraction between these two functions:

$\frac{f(x)}{g(x)}=\frac{16x^{5}-48x^{4}-8x^{3}}{8x^{2} }$

Then, we separate the denominator to operate each term in the numerator:

$\frac{16x^{5}}{8x^{2}}-\frac{48x^{4}}{8x^{2}}-\frac{8x^{3}}{8x^{2}}$

Now, we have to divide numbers and terms, remember that power dividing requires to subtract exponents and maintain the same base:

$2x^{3}-6x^{2}-x$

Therefore, the result of this function division is:

$2x^{3}-6x^{2}-x$