Question

Which of the following sets of polynomials is a vector space? Here you only need to check the closure properties:
Is the sum of any two polynomials in the set also in the set?
Is the scalar multiple of any polynomial in the set also in the set?
a.) The set of all polynomials of the form p(x)=ax^2 +bx +c, where ,a b and c are arbitrary real numbers.
b.) The set of all polynomials of degree 2.
c.) The set of all polynomials satisfying the equation p(0)=0.
d.) The set of all polynomials satisfying the equation p(0)=1.
e.) The set of all polynomials satisfying the equation p(1)=0.