Use Descartes's rule of signs to determine the possible combinations of real and complex roots for the polynomial. Then graph the function on the standard window of a graphing calculator and adjust it as needed until you're certain all real roots are in clear view. Use this screen and a list of the possible rational zeroes (rational roots theorem) to factor the polynomial and find all zeroes (real and complex). p(x) = 20x³ - 153x² - 62x + 48 A) p(x) = (x - 8)(2x + 1)(10x + 6) B) p(x) = (x + 8)(10x - 1)(2x + 6) C) p(x) = (x - 8)(5x - 2)(4x + 3) D) p(x) = (x + 8)(4x + 1)(5x + 6)

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Descartes's rule of signs and the rational roots theorem, along with graphing, help identify the real roots and their multiplicities, leading to the correct factorization in option C.

Use Descartes's Rule of Signs to Determine the Possible Combinations