Question

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

2x2 − 4x − 3 − (13/4x-3)  
2x2 − (4x − 3/13) 
 2x2 − 7x − 1
   2x2 − 7x − 5 +(x-4/4x-3)

Answer 1

I hope this helps you

Answer 2

Option 1 -
`(2x^2-4x-3)(-13)/((4x-3))`

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
`(f(x))/(g(x))`

Substitute the value in the formula,

`(f(x))/(g(x))=(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}* \text{Divisor}+\text{Remainder}`

i.e.
`(8x^3-22x^2-4)=(2x^2-4x-3)*(4x-3)+(-13)`

or in mixed fraction it is written as
`(2x^2-4x-3)(-13)/((4x-3))`

Therefore, Option 1 is correct.