Question

Please help me get this

Answer 1

`f(x) / g(x)=3 x^(2)+x+2+(3)/(5 x-1)`

Solution:

Given:

`f(x)=15 x^(3)+2 x^(2)+9 x+1`

`g(x)=5 x-1`

`f(x) / g(x)`

`$=(\left(15 x^(3)+2 x^(2)+9 x+1\right))/(5 x-1)`

If we divide
`(15 x^(3))/(5 x)=3 x^(2)` quotient and remainder is
`5 x^(2)+9 x+1`.

`$=3 x^(2)+(5 x^(2)+9 x+1)/(5 x-1)`

If we divide
`(5 x^(2))/(5 x)=x` quotient and remainder is
`10 x+1`.

`$=3 x^(2)+x+(10 x+1)/(5 x-1)`

If we divide
`(10 x)/(5 x)=2` quotient and remainder is 3.

`$=3 x^(2)+x+2+(3)/(5 x-1)`.

Therefore,
`f(x) / g(x)=3 x^(2)+x+2+(3)/(5 x-1)`.