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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 \((x+1)^3\)

 May 31, 2020
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1. The remainder is x^2 - 4x + 7.

 

2. f(x) = 36x^5 - 20x^4 + 5x^3.

 May 31, 2020

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