91Ó°ÊÓ

Find all the real zeros of the polynomial. $$P(x)=7 x^{3}+2 x^{2}-28 x-8$$

Determine the end behavior of the function. $$f(s)=\frac{7}{2} s^{5}-14 s^{3}+10 s$$

Determine together \(q(x)\) is a factor of \(p(x)\) Here, \(p(x)\) is the first polynomial and \(q(x)\) is the second polynomial. justify your answer. $$x^{3}-7 x+6 ; x+3$$

Sketch a graph of the rational function. Indicate any vertical and horizontal asymptote(s) and all intercepts. $$f(x)=\frac{1}{x-2}$$

Determine the end behavior of the function. $$f(s)=-\frac{3}{4} s^{4}+8 s^{2}-3 s-16$$

Find all the real zeros of the polynomial. $$Q(x)=x^{4}-8 x^{2}-9$$

One zero of each polynomial is given. Use it to express the polynomial as a product of linear factors over the complex numbers. You may have already factored some of these polynomials into linear and irreducible quadratic factors in the previous group of exercises. $$x^{3}-x^{2}+4 x-4 ; \text { zero: } x=1$$

Sketch a graph of the rational function. Indicate any vertical and horizontal asymptote(s) and all intercepts. $$f(x)=\frac{1}{x+3}$$

Determine together \(q(x)\) is a factor of \(p(x)\) Here, \(p(x)\) is the first polynomial and \(q(x)\) is the second polynomial. justify your answer. $$x^{3}-5 x^{2}+8 x-4 ; x-2$$

For each polynomial function, find (a) the end behavior; (b) the \(y\) -intercept; (c) the \(x\) -intercept(s) of the graph of the function and the multiplicities of the real zeros; (d) the symmetries of the graph of the function, if any; and (e) the intervals on which the function is positive or negative. Use this information to sketch a graph of the function. Factor first if the expression is not in factored form. $$f(x)=(x-1)(x+2)^{2}(x+1)$$