Okay, so i have this problem in my text, and I've almost figured it out (i think) but i need a little help(adsbygoogle = window.adsbygoogle || []).push({});

"Let V be the set of all polynomials of degree 3. Define addition and scalar multiplication pointwise. Prove that V with respect to these operations of addiont and scalar multiplication is NOT a vector space"

I have pointwise addition and pointwise scalar multiplication defined... but i'm a little stumped on why V wouldn't be a vector space

-i know that V cannot have a 0 element (0 is not a degree 3 polynomial) and thus it cannot be a vector space, but that doesn't really explain it via addition/multiplication

-also, i know that the addition of 2 degree 3 polynomials does not always result in a degree 3 polynomial ie: x^3 + (-x^3)=0 (not a degree 3 polynomial)

if anyone has any other reasons why V cannot be a vector space according to pointwise addition/scalar multiplication please let me know

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# V not vector space with degree 3 polynomials

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