1) Is the polynomial $\displaystyle p(x)=1+x+x^2$ in $\displaystyle span(1-x+2x^2, -1+x^2, -2-x+5x^2)?$

Would you approach this question like this:

$\displaystyle \lambda_1(1-x+2x^2)+\lambda_2(-1+x^2)+\lambda_3(-2-x+5x^2)=1+x+x^2$

And then just find the coefficients? If the coefficients don't exist, then the polynomial is not in the span.

2) Is $\displaystyle S=\{1+x,1-x^2,x+2x^2\}$ a spanning set for $\displaystyle \mathbb{P}_2$?

I really just need a hint for this question on how to start it up.

What exactly does it mean is it a spanning set for $\displaystyle \mathbb{P}_2$