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Question
f(x) = 2x4 − 6x3 + 2x2 − x + 2, g(x) = x + 2
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Solution
Let us denote the given polynomials as
`f(x) = 2x^4 -6x^3 + 2x^2 - x + 2`
`g(x) = x+2`
`⇒ g(x) = x-(-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(-2) = 2 (-2)^4 - 6(-2)^3 + 2(-2)^2 - (-2) + 2 `
` = 32 + 48 + 8 + 2 + 2`
` = 92`
Now we will calculate the remainder by actual division
So the remainder by actual division is 92.
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