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Question
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x .
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Solution
Let us denote the given polynomials as
`f(x) = x^3 + 3x^2 + 3x + 1`
`k(x) = 5+2x`
`⇒ k(x) = 2 {x-(-5/2)}`
We will find the remainder when f(x)is divided by k(x).
By the remainder theorem, when f(x)is divided by k(x) the remainder is
`= f(-5/2)`
` = (-5/2)^3 + 3(-5/2)^2 + 3 (-5/2)+1`
`= 125/8 + 75/4 - 15/2` + 1
` = - 27/8`
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