Given the ideal I=(x^3,x^5) of the polynomial ring Q[x] 1) 1 example of a polynomial which belongs to I and has 4 non-zero terms 2) 1 example of a polynomial which doesn't belong to I and has 3 non-zero terms.
I didn't really understand when a polynomial belongs to an ideal in this kind of a situation (x^3,x^5) An advice /explication would be enough and much appreciated.
If by term you mean coefficient then $(1+x)*x^3 + (1+x)*x^5$ is an example for the first. $1+x+x^2$ is an example for the second question