Exercise 7

Find the dimension of each.

• The space of cubic polynomials $p(x)$ such that $p(7)=0$

• The space of cubic polynomials $p(x)$ such that $p(7)=0$ and $p(5)=0$

• The space of cubic polynomials $p(x)$ such that $p(7)=0$, $p(5)=0$, and $p(3)=0$

• The space of cubic polynomials $p(x)$ such that $p(7)=0$, $p(5)=0$, $p(3)=0$, and $p(1)=0$