Question: a) Using ideas from calculus, explain why the graph of an odd-degree polynomial with real coefficients must cross the horizontal axis. (b) Without appealing to

a) Using ideas from calculus, explain why the graph of an odd-degree polynomial with real coefficients must cross the horizontal axis.

(b) Without appealing to the Fundamental Theorem of Algebra, explain why a cubic polynomial with real coefficients must factor into a product of a linear polynomial and a quadratic polynomial (both with real coefficients).

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