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 can be written as x – 0

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

⇒ p(a) = p(0)

⇒ p(0) = 0^{4} + 0^{3} - 3(0)^{2} + 3(0) + 1

⇒ p(0) = 1

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

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