91Ó°ÊÓ

Sketch the polynomial function using transformations. $$f(x)=x^{4}-1$$

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. $$2 x^{3}-9 x^{2}+7 x+6 ; \text { zero: } x=2$$

Sketch a graph of the rational function. Indicate any vertical and horizontal asymptote(s) and all intercepts. $$f(x)=\frac{-10}{x+2}$$

Find all the real zeros of the polynomial. $$f(x)=x^{5}-7 x^{4}+10 x^{3}+14 x^{2}-24 x$$

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. $$f(x)=-3(x-2)^{2}(x+1)^{2}$$

Solve the rational inequality. $$\frac{1}{x} \leq \frac{1}{2 x-1}$$

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. $$x^{4}-5 x^{3}+7 x^{2}-5 x+6 ; \text { zero: } x=2$$

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. $$x^{4}-50 ; x-5$$

Find all real solutions of the polynomial equation. $$x^{3}+2 x^{2}+2 x=-1$$

Sketch the polynomial function using transformations. $$f(x)=\frac{1}{2} x^{3}$$