My main question is the following.

Find all f in R_{<}_{=2}[x] such that f ⊥ (x^2+1)

Note: R_{<=2}[x] is the set of all polynomial of degree less than or equal to 2.

I am not sure how to do this problem as it was never explained in class, he just mentioned that you could find polynomials perpendicular to other polynomials...

Then my other question is:

-Find reasons why each of these are not examples of inner product spaces:

(a) V=R[x], with <f,g> = (fg')(0).

(b) V = M_{nxn}(R), with <A,B> = det (AB)

Any help would be greatly appreciated!!