how to prove a spanning set of polynomial I am struggling so much understanding this concept of subspace and span.
The question is, Given that 
$P2:W=\{(x+1)(ax+b)| a,b \in R\}$
show that 
$\{x^2+x, x^2+2x+1\}$
is a spanning set of $W$.
I don't know if I got this concept right, but I've tried to do things by letting 
$p(x)=x^2+x$
$q(x)=x^2+2x+1$
then multiplying them a coefficient $\alpha$ and $\beta$ each and adding to fit in with $W$.
but then I got an answer saying $a=\alpha + \beta$, $a+b = \alpha+ 2\beta, b=\beta$, which means... no solution? I am guessing? so this does not span $W$. Am I right?

Hint:  First, $W$ is a $2$-dimensional vector space (easy to see).
Now, $\{x^2+x,x^2+2x+1\}$ is linearly independent (easy to see)
Let $a=1,b=0$.  We get $x^2+x$.  Now let $a=1,b=1$.  We get $x^2+2x+1$.  
Thus $W=\operatorname{span} \{x^2+x,x^2+2x+1\}$.
. 
