Intersection of sets spanned by polynomials

[osuwp]

Let s1 be the set spanned by the polynomials: x^3+x+1, x^3-3x^2+x-2, 2x^3-1. Let s2 be the set spanned by the polynomials: x^3-1, x^2+x+1. What is the intersection of s1 and s2?

I really don't know where to begin, I don't know how to define these sets, s1 and s2. since i don't know what they are it is hard for me to find their intersection.

 

[Dick]

Not knowing how to start is not great. And and not knowing how to define s1 and s2 is worse. Can't you look that up? If {p1,p2,p3} is a set of polynomials, then the span is the set of all A1*p1+A2*p2+A3*p3 for A1, A2 and A3 real numbers (or complex, or whatever). Similarly for your second set. If you equate the two you should get some linear equations to solve.

 

[matt grime]

Perhaps you're thrown by the fact it's polynomials. If I were to say what is the intersection of the vector subspace of R^4 spanned by

(1,0,1,1), (1,-3,1,-2), (2,0,0,-1)

and the vector subspace spanned by

(1,0,0,-1) and (0,1,1,1)

wouldn't you have a section in your notes about how to do that?