Answer:
Option 1 - \((2x^2-4x-3)\frac{-13}{(4x-3)}\)
Step-by-step explanation:
Given : \(f(x)=8x^3-22x^2-4\) and \(g(x)=4x-3\)
To find : f of x over g of x.
Solution :
\(f(x)=8x^3-22x^2-4\) and \(g(x)=4x-3\)
f of x over g of x is \(\frac{f(x)}{g(x)}\)
Substitute the value in the formula,
\(\frac{f(x)}{g(x)}=\frac{8x^3-22x^2-4}{4x-3}\)
Now, We have to divide the numerator by denominator with the help of calculator.
Refer the attached figure below.
Here, Dividend is \(f(x)=8x^3-22x^2-4\)
Divisor is \(g(x)=4x-3\)
We get, Quotient is \(2x^2-4x-3\)
and Remainder is -13.
The form is \(\text{Dividend}=\text{Quotient}\times \text{Divisor}+\text{Remainder}\)
i.e. \((8x^3-22x^2-4)=(2x^2-4x-3)\times(4x-3)+(-13)\)
or in mixed fraction it is written as \((2x^2-4x-3)\frac{-13}{(4x-3)}\)
Therefore, Option 1 is correct.
