Find the unique polynomial of degree 4 that takes on values p(1) = 2 , p(2) = 1 , p(3) = 0 , p(4) = 4 , and p(5) = 0 . Write your answer in the coefficient representation.
a) p(x) = x⁴ - 7x³ + 17x² - 13x + 3
b) p(x) = -x⁴ + 7x³ - 17x² + 13x - 3
c) p(x) = x⁴ - 5x³ + 10x² - 10x + 4
d) p(x) = -x⁴ + 5x³ - 10x² + 10x - 4