Please help answer the following four questions:

Polynomials 7. Let Q(r) be a cubic polynomial and Q (1) = Q(2) = Q(4) = 0, Q(3) = 1. Determine Q(x). 8. (Optional) Let P(x) be a polynomial of degree 2020 and 1 P (1 ) = - P ( 2 ) = P ( 3 ) = . . . P(2021) = - 2021 Find P(2022). 9. Let P(x) = x3 + 4x2 + x - 6. Find a polynomial Q(x) and a constant r such that P(x) = (2 - 2)Q(2) +r 10. Let P(x) = 24 + 3x3 - 5x + 10 and D(x) = 12 - x - 2. (a) Find the quotient Q(r) and the remainder R(r) that are obtained when P(x) is divided by D(x). (b) Find partial fraction decomposition of D(x)