Question 4: Consider the polynomial equation 8x443 18a211- 2 = 0 (a) Using the Rational Root Theorem, show work to find the possible roots c of this equation (b) Using synthetic division, show work to find one rational root c. Hint: try positive c's. (c) Use the Factor Theorem to rewrite f as f (x) = (x - c)q(x) with the synthetic division you just did. (d) Using the Rational Root Theorem for q(x), show work to find possible zeros c of q (e) Using synthetic division, show work to find one rational root c2 of q. Hint: try positive c's. (f) Use the Factor Theorem to write q(x) = (x - c2)q2(x) with the new root c2 and new quotient q2. (This is two problems in one it will be separated for test purposes, with different numbers, of course)
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Question 4: Consider the polynomial equation 8x443 18a211- 2 = 0 (a) Using the Rational Root Theorem, show work to find the possible roots c of this equation (b) Using synthetic division, show work to find one rational root c. Hint: try positive c's. (c) Use the Factor Theorem to rewrite f as f (x) = (x - c)q(x) with the synthetic division you just did. (d) Using the Rational Root Theorem for q(x), show work to find possible zeros c of q (e) Using synthetic division, show work to find one rational root c2 of q. Hint: try positive c's. (f) Use the Factor Theorem to write q(x) = (x - c2)q2(x) with the new root c2 and new quotient q2. (This is two problems in one it will be separated for test purposes, with different numbers, of course)
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