Let $F$ be a field. $V$ is a vector space over $F$, consisting of all polynomias of degree less or equal to $3$ with coefficients in $F$. Does the sequence $S:\,x,(1-x^2),x^3$ span $V$ ?
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Note the dimension of $V$ is 4 and $|S|=3$ so it's impossible for $S$ to span $V$.
Indeed, you cannot generate constant polynomials using this basis.