Question

Find the remainder when x³ + 3x² + 3x + 1 is divided by x.

Answer 1

Let us denote the given polynomials as

`f(x) = x^3 + 3x^2 + 3x + 1,`

       `i(x) = x`

`⇒ i(x) = x-0,`

We will find the remainder when f(x) is divided by  i(x).

By the remainder theorem, when f(x) is divided by i(x) the remainder is

` = f(0)`

` = (0)^3 + 3(0)^2 + 3 (0) + 1`

` = 0 + 0 + 0 +1`

` = 1`