Find the remainde

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 – 1

comparing x – 1 with x – a we have here a = 1

x – 1= 0, x = 1

⇒ p(a) = p(1)

⇒ p(1) = 1⁴ + 1³ – 3(1)² + 3(1) + 1

⇒ p(1) = 1 + 1 – 3 + 3 + 1

⇒ p(1) = 3

Hence the remainder when p(x) is divided by x – 1 is 3