Question

Find the remainder when the polynomial $x^5 x^4 x^3 x^2 x$ is divided by $x^3-4x$.

Answer 1

Remainder would be
`5x^2+21`

Explanation:

Given,

Dividend =
`x^5+x^4+x^3+x^2+x`

Divisor =
`x^3-4x`

Using long division ( shown below ),

We get,

`(x^5+x^4+x^3+x^2+x)/(x^3-4x)=x^2+x+5+(5x^2+21)/(x^3-4x)`

Therefore,

Remainder would be
`5x^2+21`