# 13 find all real and complex zeros of 3 2 4 6 14 find

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13. Find all real and complex zeros of 𝑃(?) = ? 3 − ? 2 − 4? − 6 14. Find the complete factorization of 𝑃(?) = ? 4 − 2? 3 + 5? 2 − 8? + 4 15. Find a fourth-degree polynomial with integer coefficients that has zeros 3𝑖 and −1 , with −1 a zero of multiplicity 2 16. Consider the following rational functions: ?(?) = 2? − 1 ? 2 − ? − 2 , ?(?) = ? 3 + 27 ? 2 + 4 , ?(?) = ? 3 − 9? ? + 2 , ?(?) = ? 2 + ? − 6 ? 2 − 25 , ?(?) = ? 3 + 6? 2 + 9? ? + 3 a) Which of these rational functions has a horizontal asymptote? b) Which of these functions has a slant asymptote? c) Which of these functions has no vertical asymptote? d) Which of these functions has a “hole”? e) What are the asymptotes of the function ?(?) f) Graph ? = ?(?) , showing clearly any asymptotes and ? - and ? - intercepts the function may have. 17. Use synthetic division to find the quotient and remainder when ? 4 − 4? 2 + 2? + 5 is divided by ? − 2 (18-19) Sketch the graph of each function, and state its domain, range, and asymptote. Show the x - and y -intercepts on the graph. 18. ?(?) = 2 −𝑥 + 4 19. ?(?) = log 3 (? + 3) 20. a) Write the equation 6 2𝑥 = 25 in logarithmic form. b) Write the equation ln 𝐴 = 3 in exponential form. 21. Find the solution of the exponential equation, rounded to two decimal places. a) 3 4𝑥 = 3 100 b) ? 3𝑥−2 = ? 𝑥 2 c) 5 𝑥 10 + 1 = 7 d) 10 𝑥+3 = 6 . . . ? .