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Question
f(x) = 4x4 − 3x3 − 2x2 + x − 7, g(x) = x − 1
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Solution
Let us denote the given polynomials as
`f (x) = 4x^4 - 3x^3 - 2x^2 + x - 7`
`g(x) = x-1`
We have to find the remainder when f(x) is divided byg(x).
By the remainder theorem, when f(x) is divided by g(x) the remainder is
`f(1) = 4(1)^4 - 3(1)^3 - 2(1)^2 + 1-7`
` = 4 - 3- 2 + 1- 7`
` = -7`
Now we will show remainder by actual division
So the remainder by actual division is −7
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