You are correct: W is not a subspace of V.
i solved this one, but am getting an answer different from the one given in the text book.
Let V= Vector space of real polynomials
W= set of all polynomials with degree>=6 and the zero polynomial(included)
Is W a subspace of V? My answer was no.
for the following set, u+v will not belong to W for
u= x^6 +2x^5 + 1 v= -x^6 +x^5 + 2
Here both u and v belong to W but the sum of those is a polynomial of degree less than 6.
The text book says W is a subspace of V.
Am I overlooking something?