SOLUTION: When f(x)is divided by x-1, the remainder is -1; when it is divided by {{{x^2}}}, the remainder is -x-1. Find the remainder when f(x)is divided by {{{(x^2)(x-1)}}}

Question 1036408: When f(x)is divided by x-1, the remainder is -1; when it is divided by , the remainder is -x-1. Find the remainder when f(x)is divided by
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The remainder would be .
To see this, notice that the polynomial , where , will always give a remainder of -1 upon division by x-1 and a remainder of -x-1 upon division by . By using synthetic division with x - 1 as divisor, it can be easily seen that f(x) is unique in form.
By applying the usual polynomial division, the remainder after dividing by is .
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