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## Homework Statement

a) The set of real polynomials of [itex]x[/itex] divisible by [itex]x^2 + x + 1[/itex];

b) The set of differentiable functions of [itex]x[/itex] on [itex][0,1][/itex] whose derivative is [itex]3x^2[/itex]

c) all [itex]f \in F[0,2][/itex] such that [itex]x \geq |f(x)|[/itex] for [itex]0 \leq x \leq 2[/itex]

## The Attempt at a Solution

a) Yes, it's a vector space, proven with addition and scalar multiplication

b) I don't really understand what the question is saying, can someone explain to me? A function that differentiates to [itex]3x^2[/itex] is [itex]x^3[/itex]. Now what?

c) Same goes for this part, not sure what the question is saying

Thanks in advanced.