Answer
Remainder is 8
Work Step by Step
The question asks for the remainder of the polynomial P(x) divided by a first-degree polynomial.
Given $P(x) = x^{500} + 6x^{101} - x^2 - 2x + 4$ and $x-1$
By remainder theorem, dividing this polynomial by (x-c) is equivalent to P(c)
Thus substitute P(1) into the equation
$P(1) = 1^{500} + 6 (1)^{101} - 1^2 - 2(1) + 4$ = 8
Thus the remainder is 8
