Let $V=\{a_0+a_1X+\cdots+a_3X^3: a_j \in \mathbb{Q}\}$, a vector space over $\mathbb{Q}$ under the usual polynomial addition and scalar multiplication. Let $W=\operatorname{span}(\{X+1,2X-1,X^2+X\})$. Find the spanning set for V/W. Prove that your answer is correct.
I am sure that this is a simple question. The one thing that is confusing me is how to deal with quotient space. Any help is great.
Thanks in advance.