Question

Find the remainder when x³ + 3x² + 3x + 1 is divided by \[x + \pi\] .

Answer 1

Let us denote the given polynomials as

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

       `j(x) = x+pi`

`⇒ j (x) = x-(-pi),`

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

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

` = f(- pi)`

`= (- pi) ^3 + 3(-pi)^2 +3(- pi)+1`

` = -pi^3 + 3pi^2 -3pi +1`