Have I worked through this correctly ?

$\displaystyle f(x) = x^3+2x^2-x+2$

$\displaystyle |f(x)| = |x^3+2x^2-x+2|$

$\displaystyle <= |x^3|+2|x^2| +|x|+|2|$ by triangle inequality

$\displaystyle = x^3+2x^2+x+2 \text{ if } x >= 0$

$\displaystyle <= x^3+2x^3+x^3+2x^3$ <--is this last 2x^3 ok?

$\displaystyle = 6x^3$

therefore $\displaystyle f(x) = O(x^3)$

Thanks for any help