# Vector space and basis

Consider the following elements of the vector space P3 of all polynomials of degree less than or equal to 3.

p(x)= x-1, q(x)=x+x2, r(x)= 1+x2-x3

Do these three polynomials form a basis for P3?

https://brainmass.com/math/vector-calculus/vector-space-basis-11644

#### Solution Preview

No.

We know, a basis in P3 is {1, x, x2, x3}, in another word, any ...

#### Solution Summary

This shows how to determine if polynomials for a bases for P3.

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