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प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x - \frac{1}{2}\].
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उत्तर
Let us denote the given polynomials as
`f(x) = x^3 + 3x^2 + 3x + 1,`
`h(x) = x-1/2`
We will find the remainder when f(x) is divided by h(x).
By the remainder theorem, when (f(x) is divided by h(x) the remainder is
`= f (1/2)`
` = (1/2)^3 + 3 (1/2)^2 + 3 (1/2) + 1`
`= 1/8 + 3/4 + 3/2 + 1`
`= 27 /8`
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