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Question
f(x) = x3 − 6x2 + 2x − 4, g(x) = 1 − 2x
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Solution
Let us denote the given polynomials as
`f(x) = x^3 - 6x^2 + 2x - 4`
`g(x) = 1-2x`
`⇒ g(x) = -2 (x - 1/2)`
We have to 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(1/2) = (1/2)^3 -6 (1/2)^2 + 2(1/2) - 4`
` = 1/8 - 6 xx 1/4 + 2 xx 1/2 - 4`
` = 1/8 - 3/2 + 1 - 4`
` = 1/8 - 3/2 - 3`
`= - 35/8`
Now we will calculate remainder by actual division
So the remainder is `(-35)/8`.
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