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This problem trains for: AMC-10, AMC-12, Math Kangaroo 9-10, AIME.
When the polynomial:
is divided by the polynomial of degree 5:
the remainder is of the form:
where the coefficients ak can have any real values.
What is the value of:
The polynomial is equal to the divisor times the quotient plus the remainder:
Since polynomials are defined for all real numbers, we can substitute -1 for x to get:
We have that:
it means that:
The answer is: