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

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#### Solution 1

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

x+1 = 0 ⇒ x = -1

∴ Remainder = p(-1) = (-1)3 + 3(-1)2 + 3(-1) + 1

= -1 + 3 - 3 + 1

= 0

Therefore, the remainder is 0.

#### Solution 2

By long division,

Therefore, the remainder is 0.

Concept: Remainder Theorem

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