91Ó°ÊÓ

Determine whether each given value of x is a zero of the given function. See Example 1. $$x=1, \quad P(x)=x^{3}-x^{2}+x-1$$

Let \(f(x)=x^{4}-1, g(x)=x^{3}-3 x^{2}+5,\) and \(h(x)=4 x^{4}-\) \(3 x^{2}+3 x-1 .\) Find the following function values by using two different methods. See Example \(I\) $$ g(2) $$

State the degree of each polynomial equation. Find all of the real and imaginary roots to each equation. State the multiplicity of a root when it is greater than 1. $$(2 x+1)^{2}(3 x-5)^{4}=0$$

State the degree of each polynomial equation. Find all of the real and imaginary roots to each equation. State the multiplicity of a root when it is greater than 1. $$x^{4}-2 x^{2}+1=0$$

Let \(f(x)=x^{4}-1, g(x)=x^{3}-3 x^{2}+5,\) and \(h(x)=4 x^{4}-\) \(3 x^{2}+3 x-1 .\) Find the following function values by using two different methods. See Example \(I\) $$ h\left(\frac{1}{2}\right) $$

State the degree of each polynomial equation. Find all of the real and imaginary roots to each equation. State the multiplicity of a root when it is greater than 1. $$4 x^{4}-4 x^{2}+1=0$$

Find a polynomial equation with real coefficients that has the given roots. $$-3,3$$

Find a polynomial equation with real coefficients that has the given roots. $$-4,2$$

Find a polynomial equation with real coefficients that has the given roots. $$-2 i, 2 i$$

Find a polynomial equation with real coefficients that has the given roots. $$-4 i, 4 i$$