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Suppose p0, p1, . . . , pm are polynomials in P(F) such that the degree...

Suppose p0, p1, . . . , pm are polynomials in P(F) such that the degree of pj is j for j = 0, . . . , m. Show that p0, p1, . . . , pm is a basis of Pm(F). (Hint: Show that p0, . . . , pm spans
Pm(F) and deduce that this is enough. Also, keep in mind that the degree of 0 is −∞ by definition.)

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