91Ó°ÊÓ

Find a polynomial function \(P(x)\) having leading coefficient 1, least possible degree, real coefficients. and the given zeros. 6 and \(-2\)

Find each quotient when \(P(x)\) is divided by the specified binomial. $$P(x)=x^{3}+2 x^{2}-17 x-10 ; \quad x+5$$

Find a polynomial function \(P(x)\) having leading coefficient 1, least possible degree, real coefficients. and the given zeros. \(-3,2,\) and \(i\)

Solve each equation analyrically for all complex solutions, giving exact forms in your solution set. Then graph the left side of the equation as \(Y_{1}\) in the suggested viewing window and, using the capabilities of vour calculater, suppert the real solutions. $$\begin{aligned}&x^{4}-15 x^{2}-16=0\\\&[-5,5] \text { by }\lfloor- 100,100\rfloor\end{aligned}$$

Give a short written answer. The graphs of \(f(x)=x^{n}\) for \(n=3,5,7, \ldots\) resemble each other. As \(n\) gets larger, what happens to the graph?

Find a polynomial function \(P(x)\) having leading coefficient 1, least possible degree, real coefficients. and the given zeros. \(1+\sqrt{2}, 1-\sqrt{2},\) and 3

Find each quotient when \(P(x)\) is divided by the specified binomial. $$P(x)=x^{4}+4 x^{3}+2 x^{2}+9 x+4 ; \quad x+4$$

Solve each equation analyrically for all complex solutions, giving exact forms in your solution set. Then graph the left side of the equation as \(Y_{1}\) in the suggested viewing window and, using the capabilities of vour calculater, suppert the real solutions. $$\begin{aligned}&9 x^{4}+35 x^{2}-4=0\\\&[-3,3] \text { by }[-10,100]\end{aligned}$$

Solve each equation analyrically for all complex solutions, giving exact forms in your solution set. Then graph the left side of the equation as \(Y_{1}\) in the suggested viewing window and, using the capabilities of vour calculater, suppert the real solutions. $$\begin{aligned}&x^{3}-x^{2}-64 x+64=0\\\&[-10,10] \text { by }[-300,300]\end{aligned}$$

Find a polynomial function \(P(x)\) having leading coefficient 1, least possible degree, real coefficients. and the given zeros. \(1-\sqrt{3}, 1+\sqrt{3},\) and 1