Answer the following questions about the equation below. \( 8 x^{3}+34 x^{2}-29 x+5=0 \) (a) List all rational roots that are possible according to the Rational Zero Theorem. Choose the correct answer below. A. \( \pm 1, \pm 2, \pm 4, \pm 8, \pm \frac{1}{5}, \pm \frac{2}{5}, \pm \frac{4}{5}, \pm \frac{8}{5} \) C. \( \pm 1, \pm 5 \) D. \( \pm 1, \pm 5, \pm \frac{1}{2}, \pm \frac{5}{2}, \pm \frac{1}{4}, \pm \frac{5}{4}, \pm \frac{1}{8}, \pm \frac{5}{8} \) (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 (Simplify your answer.)

Find the greatest common factors (GCF) of the following numbers. 1. Using Venn diagram method a. 12,18 b. 24,64 c. \( 45,63,99 \) 2. Using prime factorization method a. 24,54 b. 108,104 c. \( 180,270,1,080 \)

Solve. \( 4 c^{3}-20 c^{2}=56 c \)

8) Una persona tarda 3 días en pintar una casa trabajando 8 horas diarias. ¿Qué parte de la casa pinta en \( \frac{x}{2} \) horas? A) \( \frac{48}{x} \) B) \( \frac{3 x}{2} \) C) \( \frac{6}{x} \) D) \( \frac{x}{6} \) E) \( \frac{x}{48} \)

La ecuación de una circunferencia con centro en el origen y radic a. \( x^{2}+y^{2}=16 \) b. \( x^{2}+y^{2}=4 \) c. \( x+y=16 \) d. \( x+y=4 \)

Find all solutions of the equation in the interval \( [0,2 \pi) \). \( -\cot x-1=\csc x \) Write your answer(s) in radians in terms of \( \pi \). If there is more than one solution, separate them with commas. \( x=\square \)