Answer :

Let p(x) = x^{3} + 3x^{2} + 3x + 1

As we know by Remainder Theorem,

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

⇒ Remainder of p(x) when divided by x + π is p(–π)

p(–π) = (–π)^{3}+ 3(–π)^{2}+ 3(–π) + 1

⇒ p(–π)= –π^{3} + 3π^{2} –3π + 1

∴ Remainder of x^{3} + 3x^{2} + 3x + 1 when divided by x+ π is –π^{3} + 3π^{2} –3π + 1

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