(12 pts) Let P(x) = x + ax+ + bx + cx? + dx +e. P(4) = P(5) = P(6)=P(7)=P(8) = 0. What is the value of a - b+c-d+e? Numerically the answer is somewhat large, but it can be represented easily as a sum...

(12 pts) Let P(x) = x + ax+ + bx + cx? + dx +e. P(4) = P(5) = P(6)=P(7)=P(8) = 0. What is the value of a - b+c-d+e? Numerically the answer is somewhat large, but it can be represented easily as a sum of terms, where the terms are a product of 1 or more small integers. You may leave your answer in this form, instead of calculating it out. (Note: This is a challenging question. One little hint is that ifr and s are roots of a polynomial, then (x - )(x - s) is a factor of that polynomial.)