Denote the set of all even polynomials of degree less than or equal to 4. Trivially the zero polynomial belongs to Besides, for all for all and for all

This means that is a subspace of

Similar arguments.b) Odd polynomials of degree less than or equal to 4

Notice that the zero polynomial has not degree 4.c) Polynomials of degree 4

Choose for example andQuestion 2: Give two polynomials that span the space of all polynomials in one variable x of degree less than or equal to 1