Find the remainder on dividing the polynomial x⁴ + x³ -3x² + 3x + 1 by the following monomial expression:

x

We will find remainder using remainder theorem which states that

If a polynomial p(x) is divided by a polynomial x – a then the remainder is p(a)

Let p(x) = x⁴ + x³ - 3x² + 3x + 1

x can be written as x – 0

comparing x – 0 with x – a we have here a = 0

⇒ p(a) = p(0)

⇒ p(0) = 0⁴ + 0³ - 3(0)² + 3(0) + 1

⇒ p(0) = 1

Hence the remainder when p(x) is divided by x is 1