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$P_3$ is the vector space of polynomials in $x$ of degree three or less with real coefficients. Which of the following are bases for $P_3$?

$\{1, x, x^2, x^3\}$

$\{x, x^2, x^3\}$

$\{1, 1+x, 1+x^2, 1+x^3\}$

$\{x^3,1-x, 1+x^2, x+x^2\}$

All of the above are bases for $P_3$.

Choices 'A' and 'C' are both bases for $P_3$.