Find the remainder when `f(x)=x^3-6x^2+2x-4` is divided by `g(x)=3x-1.`

Explanation

Solution
Here, `g(x) = 3x - 1`
To apply Remainder theorem, `(3x - 1)` should be converted to `(x-a)` form
`:.3x-1= 1/3(3x - 1)=x-1/3:.g(x)=(x-1/3)`
By remainder theorem, `r(x) = p(a) = p(1/3)`
`p(x) = x³ - 6x² + 2x - 4 ⇒ p(1/3)=(1/3)^3-6(1/3)^2+2(1/3)-4`
=`1/27-6/9+2/3-4=(1-18+18-108)/27=-107/27`
:. the remainder p`(1/3)=-107/27`