I've noticed that most of my problems come, when I try to solve spaces of polynomials rather than real numbers.

Please, help.

T: P3(all polynomials of third degree or less)-->R, T(a+bx+cx^2+dx^3)=a

Find the kernel of the linear transformation.

My approach starts as follows:

According to my book, Elementary Linear Algebra by Larson and Falvo, the kernel of linear transformations is found by equating the right hand side of the T function to 0.

Then, a=0. But, I can't make anything out of it.

Most of the examples are very straight forward and in R. There are no examples on P spaces.