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1. Let f(x) be a polynomial such that f(0)=4, f(1)=5, and f(2)=10. Find the remainder when f(x) is divided by x(x-1)(x-2).
2. Find a polynomial f(x) of degree 5 such that both of these properties hold:
f(x) is divisible by \(x^3\)
f(x)+2 is divisible by \((x+1)^3\)