`f(x)=3x^4+2x^3-(x^2)/3-x/9+2/(27), g(x)= x+2/3`

Explanation

"We have
`f(x) = 3x^4 +2x³ - x²/3 -x/9 + 2/27, g(x) = x+2/3`
Therefore, by remainder theorem when `f(x)` is divided by `g(x) = x- (-2/3)`, the remainder is equal to `f(-2/3)`
Now, `f(x)=3x^4 + 2x³-x²/3- x/9 +12/27`
=`f(-2/3)=3(-2/3)^4+2(-2/3)^3-(-2/3)^2/3-(-2/3)/9+2/27`
=`16/27-16/27-4/27+2/27+2/27`

=`(16-16-4+2+2)/27`
=`0/27=0`
Hence, required remainder is `0`.

"