Part A) :
Notice that . So . So . Now evaluate this polynomial in and you have the answer.
B) What's the definition of a linear transformation?
Edit : C) We want to know for what polynomials in the relation holds. For it, we chose the general form of polynomials that are in . .
We know that , so .
So . Clearly , however . Are you sure the question reads?Show that Ker(T) = P1