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Question
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
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Solution 1
Let p(x) = x3 + 3x2 + 3x + 1
5 + 2x = 0
⇒ 2x = -5
`⇒ x = -5/2`
`therefore "Remainder "= (-5/2)^3 + 3(-5/2)^2 + 3(-5/2) + 1`
`= -125/8+75/4-15/2+1`
`= -27/8`
Therefore, the remainder is `-27/8" ."`
Solution 2
By long division,
Therefore, the remainder is `-27/8" ."`
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