91Ó°ÊÓ

Use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero. Adjust the table to approximate the zeros of the function. Use the zero or root feature of the graphing utility to verify your results. \(f(x)=x^{3}-3 x^{2}+3\)

Find the values of \(b\) such that the function has the given maximum or minimum value. \(f(x)=x^{2}+b x+26 ;\) Minimum value: 10

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. \(f(x)=-5 x^{3}+x^{2}-x+5\)

Briefly explain what it means for a divisor to divide evenly into a dividend.

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative zeros of the function. \(f(x)=3 x^{3}+2 x^{2}+x+3\)

Find the values of \(b\) such that the function has the given maximum or minimum value. \(f(x)=x^{2}+b x-25 ;\) Minimum value: -50

Determine whether the statement is true or false. Justify your answer. \(-i \sqrt{6}\) is a solution of \(x^{4}-x^{2}+14=56\).

Briefly explain how to check polynomial division, and justify your reasoning. Give an example.

Use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero. Adjust the table to approximate the zeros of the function. Use the zero or root feature of the graphing utility to verify your results. \(f(x)=0.11 x^{3}-2.07 x^{2}+9.81 x-6.88\)

Find the constant \(c\) such that the denominator will divide evenly into the numerator. \(\frac{x^{3}+4 x^{2}-3 x+c}{x-5}\)