91Ó°ÊÓ

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

Solve the inequality. $$\frac{2 x+5}{x^{2}+2 x-35} \geq 0$$

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

All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form. $$P(x)=x^{3}-6 x^{2}+12 x-8$$

Factor the polynomial completely, and find all its zeros. State the multiplicity of each zero. $$P(x)=x^{2}+25$$

Graphing Factored Polynomials Sketch the graph of the polynomial function. Make sure your graph shows all intercepts and exhibits the proper end behavior. $$P(x)=-(2 x-1)(x+1)(x+3)$$

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

Solve the inequality. $$\frac{4 x^{2}-25}{x^{2}-9} \leq 0$$

Factor the polynomial completely, and find all its zeros. State the multiplicity of each zero. $$P(x)=4 x^{2}+9$$

All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form. $$P(x)=x^{3}+12 x^{2}+48 x+64$$