91Ó°ÊÓ

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

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. $$3 x^{3}-48 x-4 x^{2}+64 ; x+4$$

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. $$x^{4}+4 x^{3}-x^{2}+16 x-20 ; \text { zero: } x=-5$$

Solve the rational inequality. $$\frac{3}{x-1} \leq 2$$

Find all real solutions of the polynomial equation. $$x^{3}-6 x^{2}+5 x=-12$$

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

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. $$x^{3}+9 x+x^{2}+9 ; x+1$$

Sketch a graph of the rational function. Indicate any vertical and horizontal asymptote(s) and all intercepts. $$h(x)=\frac{-9}{(x-3)^{2}}$$

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. $$f(x)=3 x^{4}-6 x^{3}+3 x^{2}$$

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. $$x^{4}-6 x^{3}+9 x^{2}-24 x+20 ; \text { zero: } x=5$$