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