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**1. The problem statement, all variables and given/known data**

1) The set H of all polynomials p(x) = a+x^3, with a in R, is a subspace of the vector space P sub6 of all polynomials of degree at most 6. True or False?

2) The set H of all polynomials p(x) = a+bx^3, with a,b in R, is a subspace of the vector space P sub6 of all polynomials of degree at most 6. True or False?

**2. Relevant equations**

Eh.. not sure?

**3. The attempt at a solution**

Once more, not too sure. I've been pouring over my Linear Algebra book, but it seems so abstract... I was under the impression that as long as the polynomial didn't have a lower power than the vector space [number] that the polynomial would be in the subspace of the given vector space :\

Does the coefficient have anything to do with it?

Some properties (if they help?): A subspace of a vector space V is a subset H of V that has 3 properties:

a) The zero vector if V is in H.

b) H closed under vector addition

3) H closed under scalar multiplication..

I've already gotten #1 wrong (the answer was false) - I'd like to know why though :(

Any help would be awesome!