I have a question about vector space. I need to prove, whether the set of polynomials of degree at least 3 is a vector space or not?
1 Answer
What is the degree of the $0$ polynomial? Assuming you can skirt this issue, you might note the lack of closure (in the manner suggested by André Nicolas). For example, here are two polynomials with degree at least three, for which the sum is a polynomial that does not have degree at least three:
$x^3 + x$ and $-x^3$. (Observe each has degree three.)
The sum of these polynomials is $x$, which is a polynomial of degree $1 < 3$.
Answer: Nope.