Let P3 = {ao+a₁x + a₂x² + 3x³|ao, a₁, 02, 03 € R} be the vector space of polynomials of degrees at most 3 with real coefficients. Is {2, (5-x), (6+ x)², (8 − x)³} a basis of P3? Justify your answer.

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A: Since, dimension of a vector space is equal to number of elements in basis of vector space.

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Q: Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² +…

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