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http://en.wikipedia.org/wiki/Vector_space#Definition

you have to check it for the axioms and see if they are true or not

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Is that space closed under addition

right...as stated it is not a vector space...no zero vector and no closure of addition

the zero vector has to be just the number 0
0 is not a 5th degree polynomial

\[(x^5+3x)+(-x^5+x^2)=3x-x^2\]
which is not a 5th degree polly

further more,
\[x^5-2x+(-x^5)\] does not have degree 5, so it is not closed under addition

what zarkon said

ok that makes sense so what is the differance in saying it has fifth degree and fifth degree or less

is one a vector and one is not and why

5th degree or less is a vector space

use the difinition I provided in my first post

i know it has to adhere to the list of axioms but can you explain it a little.

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