2. Factoriza todo lo posible los siguientes polinomios y señala las raíces, los ceros o las soluciones encontradas: a) \( P(x)=x^{3}+4 x^{2}+x-6 \) b) \( Q(x)=5 x^{2}-7 x-6 \) c) \( R(x)=3 x^{3}-5 x^{2}+2 x \) d) \( S(x)=2 x^{3}+x^{2}-8 x-4 \) e) \( U(x)=2 x^{3}-5 x^{2}-2 x-3 \)

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the \( x \)-axis or touches the \( x \)-axis and turns around at each zero. \( f(x)=x^{3}+3 x^{2}-16 x-48 \) Determine the behavior of the function at each zero. Select the correct choice below and, if necessary, fill in the answer boxes within your choice. A. The graph crosses the \( x \)-axis at \( x=\square \). The graph touches the \( x \)-axis and turns around at \( x=\square \). (Type integers or decimals. Simplify your answers. Use a comma to separate answers as needed.) B. The graph crosses the \( x \)-axis at all zeros. C. The graph touches the \( x \)-axis and turns around at all zeros.

dent Name: Which graph shows the solution of \( -6(n-1)<3 \) and \( 2(n+1)>0 \) ?

Write the expression as a single logarithm. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z \) A. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z=\log _{c} \frac{y^{7} z^{1 / 3}}{x^{6}} \) B. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z=\log _{c} \frac{x^{6} y^{7}}{z^{3}} \) O. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z=\log _{c} \frac{x^{6} y^{7}}{z^{1 / 3}} \) O. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z=\log _{c} \frac{x^{6} z^{1 / 3}}{y^{7}} \)

1) \( \left(4 x^{2}+5\right)\left(x^{2}-2\right)\left(x^{2}+2\right)=0 \) A) \( \left\{\frac{i \sqrt{5}}{2},-\frac{i \sqrt{5}}{2}, \sqrt{2},-\sqrt{2}, i \sqrt{2},-i \sqrt{2}\right\} \) B) \( \left\{\frac{i \sqrt{10}}{2},-\frac{i \sqrt{10}}{2}, \sqrt{2},-\sqrt{2}, i \sqrt{2},-i \sqrt{2}\right\} \) C) \( \left\{\frac{i \sqrt{15}}{3},-\frac{i \sqrt{15}}{3}, i \sqrt{3},-i \sqrt{3}, i \sqrt{2},-i \sqrt{2}\right\} \) D) \( \left\{\right. \) mult. \( \left.2, \frac{i \sqrt{5}}{2},-\frac{i \sqrt{5}}{2}, \sqrt{2},-\sqrt{2}\right\} \)

The following function is given. \( f(x)=3 x^{3}-7 x^{2}-75 x+175 \) a. List all rational zeros that are possible according to the Rational Zero Theorem. Choose the correct answer below.