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