Question

Find the remainder when x³ + 3x² + 3x + 1 is divided by \[x - \frac{1}{2}\].

Answer 1

Let us denote the given polynomials as

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

`h(x) = x-1/2`

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

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

`= f (1/2)`

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

`= 1/8 + 3/4 + 3/2 + 1`

`= 27 /8`