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Question
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
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Solution 1
Let p(x) = x3 + 3x2 + 3x + 1
x + π = 0 ⇒ x = -π
∴ Remainder = (-π)3 + 3(-π)2 - 3(-π) + 1
= -π3 + 3π2 - 3π + 1
Therefore, the remainder is -π3 + 3π2 - 3π + 1.
Solution 2
By long division,
Therefore, the remainder is -π3 + 3π2 - 3π + 1.
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