Answer :

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) = x^{4} + x^{3} - 3x^{2} + 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) = 1^{4} + 1^{3} – 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

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