Question

Find the remainder when x³ + 3x² + 3x + 1 is divided by 5 + 2x .

Answer 1

Let us denote the given polynomials as

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

        `k(x) = 5+2x`

`⇒ k(x) = 2 {x-(-5/2)}`

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

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

`= f(-5/2)`

` = (-5/2)^3 + 3(-5/2)^2 + 3 (-5/2)+1`

`= 125/8 + 75/4 - 15/2` + 1

` = - 27/8`