Problem: Determine if the set
\[
B = \left\{ 1, x^2 - x + 5, 4x^3 - x^2 + 5x, 3x + 2 \right\}
\]
is a basis for the vector space of polynomials in $x$ of degree at most $4$. Is this set a basis for the vector space of polynomials in $x$ of degree $\leq 3$?
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