Good day to all,

I have read the section on general vector spaces and there was a passing by mention of polynomials as a vector space. Furthermore, my teacher has mentioned nothing about polynomials in relation to vector spaces. As I was doing the end of chapter exercises, I came across two questions that I do not understand:

Question 1:

The set of all polynomials that take the value 1 at the point 0 is a vector space. (True or false)

Question 2:

The set of all polynomials that take the value 0 at the point 1 is a vector space. (True or false)

Question 3:The set of all polynomials of the form p(t)=a+bt+ct^2+t^3

I know that to determine if something is a vector space one would have to go through the list of axioms and see if any fail. For the third question, I suspect that it is not as it does contain the zero element since the coefficient of t^3 is 1<>0. As for the other questions I simply do not know or am not seeing it.

Lastly, I was wondering if someone has any suggestions as to a good textbook that may elaborate on the topic of polynomials and vector spaces.

Kindest regards