Question

Let f(x) = 16x5 – 48x4 – 8x3 and g(x) = 8x2. Find f of x over g of x. a) 2x2 + 6x + 1 b)2x2 – 6x – 1 c)2x3 + 6x2 + x d)2x3 – 6x2 – x

Answer 1

`\boxed{\boxed{(f(x))/(g(x))=2x^3-6x^2-x}}`

Explanation:

Here given that,

`f(x) = 16x^5-48x^4-8x^3\\\\g(x) = 8x^2`

So
`(f(x))/(g(x))` will be,

`(f(x))/(g(x))=(16x^5-48x^4-8x^3)/(8x^2)`

Applying single division,

`(16x^5-48x^4-8x^3)/(8x^2)=(16x^5)/(8x^2)-(48x^4)/(8x^2)-(8x^3)/(8x^2)`

Simplifying further,

`(16x^5)/(8x^2)-(48x^4)/(8x^2)-(8x^3)/(8x^2)=2x^3-6x^2-x`

Answer 2

The answer is d)2x3 – 6x2 – x.

It is given:

`f(x)=16 x^(5)-48 x^(4) -8 x^(3)`

`g(x)=8 x^(2)`

We should find:

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

So, we just need to replace it in the equation:

`f( (f(x))/(g(x)) )= (16 x^(5)-48 x^(4) -8 x^(3))/(8 x^(2))`

Let's now separate each member of equation:

`f( (f(x))/(g(x)) )= (16 x^(5))/(8 x^(2)) - (48 x^(4))/(8 x^(2)) - (8 x^(3))/(8 x^(2)) = (16)/(8) x^(5-2) -(48)/(8) x^(4-2) -(8)/(8) x^(3-2)`


`f( (f(x))/(g(x)) )=2 x^(3) -6 x^(2) -x`