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

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#### Solution 1

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

x + π = 0 ⇒ x = -π

∴ Remainder = (-π)^{3} + 3(-π)^{2} - 3(-π) + 1

= -π^{3} + 3π^{2} - 3π + 1

Therefore, the remainder is -π^{3} + 3π^{2} - 3π + 1.

#### Solution 2

By long division,

Therefore, the remainder is -π^{3} + 3π^{2} - 3π + 1.

Concept: Remainder Theorem

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