Question

Let f(x) = 8x3 − 22x2 − 4 and g(x) = 4x − 3. Find f of x over g of x.

Answer 1

Given that $f(x)=8x^3-22x^2-4$ and $g(x)=4x-3$

Question says to find f of x over g of x which simply means divide value of f(x) by value of g(x)

Dividing them gives:

$\frac{f(x)}{g(x)}=\frac{8x^3-22x^2-4}{4x-3}$

Denominator is already in factored form which can't divide numerator means it can't be simplified more.

Hence final answer is $\frac{f(x)}{g(x)}=\frac{8x^3-22x^2-4}{4x-3}$.

other part of question is not clear so i will skip them.

Answer 2

Answer:

The correct answer is the first one.

Step-by-step explanation:

We have the functions $f(x) = 8x^3-22x^2-4$ and $g(x) = 4x-3$. Then, the fraction is

$\frac{f(x)}{g(x)} = \frac{8x^3-22x^2-4}{4x-3}$.

If we want to give a ‘‘simplified’’ expression for this quotient we must do a a division of polynomials. The algorithm is the analogue for the division of integers. Attached there is an image of the procedure.

After the completion of the division algorithm we obtain

$\frac{f(x)}{g(x)} = \frac{(4x-3)(2x^2-4x-3)-13}{4x-3} = 2x^2-4x-3 - \frac{13}{4x-3}$.