Math 180 Quiz #5 – Sections 3.4, 3.5, 3.6, XXXXXXXXXXpoints) (Make sure to show all of your work) [Section 3.4] Find all rational zeros of P (x) = 2x3 +7x2−7x−12 and write the polynomial in factored...

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Math 180 Quiz #5 – Sections 3.4, 3.5, 3.6, 4.1 (55 points) (Make sure to show all of your work) [Section 3.4] Find all rational zeros of P (x) = 2x3 +7x2−7x−12 and write the polynomial in factored form. Include a list of all possible rational zeros and all steps to find them (including testing at least 3 possibilities using synthetic division for the rational zeros). (14 points) [Section 3.5] Find a polynomial Q of degree 4 with integer coefficients and zeros −2i and 4 + i. (13 points) [Section 3.6] Sketch the graph of r(x) = 2x2 + 7x− 4 2x + 4 . State all intercepts, asymptotes, and find the behavior near the vertical asymptote(s). Then find the domain and estimate the range of the function. (20 points) x y [Section 4.1] Sketch the graph of g(x) = −2x−6 + 3 by applying transformations to f(x) = 2x. Include at least 3 correct points on the graph. State the domain, range, and horizontal asymptote of g. (8 points) x y [Extra Credit] For P (x) = 9x4 − 27x3 + 14x2 + 12x− 8: (i) Use Descartes’ Rule of Signs to determine how many positive and how many negative real zeros the polynomial can have. Then determine the possible total number of real zeros. (7 points) (ii) Show that a = −1 is a lower bound and b = 3 is an upper bound for the real zeros of the polynomial. (4 points)