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