91Ó°ÊÓ

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

Sketch a graph of the rational function. Indicate any vertical and horizontal asymptote(s) and all intercepts. $$f(x)=\frac{-12}{x+6}$$

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

Find all the real zeros of the polynomial. $$h(x)=x^{4}+3 x^{3}-8 x^{2}-22 x-24$$

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. $$x^{5}-3 x^{3}+2 x-8 ; x-4$$

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. $$2 x^{3}-9 x^{2}-11 x+30 ; \text { zero: } x=5$$

Solve the rational inequality. $$\frac{4-x}{x-1}>x$$

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

Solve the rational inequality. $$\frac{-8}{x+3}<-2 x$$

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. $$-2 x^{4}-7 x^{3}+5 ; x+2$$