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Question
f(x) = 9x3 − 3x2 + x − 5, g(x) = \[x - \frac{2}{3}\]
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Solution
Let us denote the given polynomials as
`f(x) = 9x^2 - 3x^2 + x -5`
`g(x) = x2/3`
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(2/3) = 9(2/3)^2 - 3 (2/3)^2 + (2/3) - 5`
`= 9 xx 8 /27 - 3 xx 4/9 + 2/3 - 5`
` = 8/3 - 4/3 + 2/3 - 5`
`= -3`
Remainder by actual division
Remainder is −3
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