Find the remainder when x^3 +3x^2 +3x+1 is divided by x+π.

Given that the polynomial x³+3x²+3x + 1 is divided by x+π

Let P(x) = x³+3x²+3x + 1

According to the remainder theorem, when a polynomial, P(x) is divided by a linear polynomial, x−a, the remainder of that division will be equivalent to P(a).

Thus, if x³+3x²+3x + 1 is divided by the linear polynomial x+π, the remainder of that division will be equivalent to P(-π)

Hence, the remainder = P(-π) = (-π)³+3(-π)²+3(-π) + 1

= -π³+3π²-3π+1

Therefore, when x³+3x²+3x + 1 is divided by x+π, we get the remainder -π³+3π²-3π+1.