91Ó°ÊÓ

Find the quotient and remainder using long division. $$\frac{x^{3}+2 x^{2}-x+1}{x+3}$$

Graphing Factored Polynomials Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$P(x)=(2-x)(x+5)$$

Graphing Quadratic Functions A quadratic function \(f\) is given. (a) Express \(f\) in standard form. (b) Find the vertex and \(x\) and \(y\) -intercepts of \(f .\) (c) Sketch a graph of \(f .\) (d) Find the domain and range of \(f\). $$f(x)=x^{2}-2 x+2$$

Using Transformations Use transformations of the graph of \(y=1 / x\) to graph the rational function, and state the domain and range. $$s(x)=\frac{-2}{x-2}$$

Solve the inequality. $$x^{2}(7-6 x) \leq 1$$

Using Transformations Use transformations of the graph of \(y=1 / x\) to graph the rational function, and state the domain and range. $$t(x)=\frac{2 x-3}{x-2}$$

Find the quotient and remainder using long division. $$\frac{4 x^{3}+2 x^{2}-2 x-3}{2 x+1}$$

Graphing Factored Polynomials Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$P(x)=-x(x-3)(x+2)$$

Graphing Quadratic Functions A quadratic function \(f\) is given. (a) Express \(f\) in standard form. (b) Find the vertex and \(x\) and \(y\) -intercepts of \(f .\) (c) Sketch a graph of \(f .\) (d) Find the domain and range of \(f\). $$f(x)=-x^{2}+6 x+4$$

A polynomial \(P\) is given. (a) Find all zeros of \(P\), real and complex. (b) Factor \(P\) completely. $$P(x)=x^{6}-1$$