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Question
f(x) = 4x3 − 12x2 + 14x − 3, g(x) 2x − 1
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Solution
Let us denote the given polynomials as
`f(x) = 4x^2 - 12x^3 - 12x^2 + 14x - 3,`
`g(x) = 2x - 1`
`⇒ 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) = 4(1/2)^3 - 12(1/2)^2 + 14 (1/2) - 3`
` = 4 xx 1/8 - 12 xx 1/4 + 14 xx 1/2 - 3`
` = 1/2 -3 + 7 - 3`
`= 3/2`
Now we will calculate the remainder by actual division
So the remainder by actual division is `3/2` .
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