Answer the following questions about the equation below. \( 12 x^{3}+53 x^{2}-34 x+5=0 \) (a) List all rational roots that are possible according to the Rational Zero Theorem. Choose the correct an A. \( \pm 1, \pm 5 \) B. \( \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12 \) C. \( \pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12, \pm \frac{1}{5}, \pm \frac{2}{5}, \pm \frac{3}{5}, \pm \frac{4}{5}, \pm \frac{6}{5}, \pm \frac{12}{5} \) (b) Use synthetic division to test several possible rational roots in order to identify one actual root. One rational root of the given equation is \( \square \frac{1}{2}, \pm \frac{5}{2}, \pm \frac{1}{3}, \pm \frac{5}{3}, \pm \frac{1}{4}, \pm \frac{5}{4}, \pm \frac{1}{6}, \pm \frac{5}{6}, \pm \frac{1}{12}, \pm \frac{5}{12} \) (Simplify your answer.)

C) \( \left(4 x^{2}+x-3\right) \div(x-3) \) E) \( \left(x^{4}+x^{3}-3 x^{2}-4 x-4\right) \div(x+3) \) H) \( \left(3 x^{2}+4 x-x^{4}-2 x^{3}-4\right) \div(x+2) \) O) \( \left(2 x^{5}-2 x^{3}+4 x^{2}-3\right) \div(x+1) \) P) \( \left(-x^{4}+2 x^{5}-2 x-3 x^{2}+1\right) \div(x-2) \) T) \( \left(-25-4 x^{4}-3 x^{2}+4 x\right) \div(x-4) \) R) \( \left(2 x^{3}+5 x^{2}-4 x-5\right) \div(2 x+1) \)

Using practical examples, discuss the barriers to effective listening.

How can prosecutors most directly influence law enforcement activity? Through their adherence to ethical standards Through their screening function Through their promotion of financial accountability Through their role as litigators

Find all solutions of the equation in the interval \( [0,2 \pi) \). \( \tan \theta=4 \) If there is more than one solution, separate them with commas. Do not round any intermediate computations. Give your answer(s) in radians, and round your answer(s) to the nearest hundredth.

Consider a sample with a mean equal to 1300 and a standard deviation equal to 350 . Calculate the standardized values for the following values. a. 1175 b. 1525 c. 1300 a. The standardized value of 1175 is \( \square \). (Round to two decimal places as needed.)