Hi, i'm having trouble with the following question.

In this question
Pn denotes the space of real polynomials of
n or less. Find the rank and nullity of the following
linear maps.

D : P5 P5, where (Dp)(t) = p(t) + p(t),
D2, where D is defined as in 3a,
E : P5 P5, where (Ep)(t) = p(t + 2),

S : P5 P10, where (Sp)(t) = p(t2 + 1).

Any help would be greatly appreciated.