Question:
The polynomial
1. P 3 is a vector space of polynomials in x of degree three or less and Dx(p(x)) = the derivative of p(x) is a transformation from P 3 to P 2.
a. the nullity of Dx is two.
b. The polynomial 2x + 1 is in the kernel of Dx.
c. The polynomial 2x + 1 is in the range of Dx.
d. The kernel of Dx is all those polynomials in P 3 with zero constant term.
e. The rank of Dx is three.
Please explain the reasoning behind the proper choice.