Question

Let R5[t] be the vector space of all polynomials in t of degree 4 or less with real coefficients. Which of the following subsets are subspaces?

I know how to test if something is a subspaces, just not sure how to do it with for these polynomial equations.

a.) {p(t)|the constant term of p(t) is 1}


e.) {p(t)|the degree of p(t) is 3}

Answer 1

a) If you take two polynomials p1(t) and p2(t) that have a constant term 1 and take the linear combination

a p1(t) + b p2(t)

then what is the constant term of that linear combination? For arbitrary a and b does this then belong to the set of all the 4th degree polynomials that have a constant term of 1?