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Question
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x.
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Solution
Let us denote the given polynomials as
`f(x) = x^3 + 3x^2 + 3x + 1,`
`i(x) = x`
`⇒ i(x) = x-0,`
We will find the remainder when f(x) is divided by i(x).
By the remainder theorem, when f(x) is divided by i(x) the remainder is
` = f(0)`
` = (0)^3 + 3(0)^2 + 3 (0) + 1`
` = 0 + 0 + 0 +1`
` = 1`
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