91Ó°ÊÓ

Simplify. Classify each result by number of terms. $$ \left(-3 x^{3}+7 x^{2}-8\right)-\left(-5 x^{3}+9 x^{2}-8 x+19\right) $$

Use synthetic division to determine whether each binomial is a factor of \(3 x^{3}+10 x^{2}-x-12\). $$ x-4 $$

Write a polynomial function in standard form with the given zeros. $$ -2,-1,3,4 $$

a. Geometry Eight points lie on a circle. How many triangles can you make using three of the points as vertices? b. How many pentagons can you make using five points as vertices? c. Reasoning Explain why your answers to parts (a) and (b) should be the same.

Find a fourth-degree polynomial function with zeros \(1,-1, i,\) and \(-i .\) Write the function in both factored form and standard form.

Graph each function to find the zeros. Rewrite the function with the polynomial in factored form. $$ y=x^{4}-10 x^{2}+9 $$

Which of the following, when multiplied by \(x-1,\) results in a cubic polynomial whose standard form has three terms? \(\begin{array}{llll}{\text { A. }(x-1)^{2}} & {\text { B. } x^{2}-x} & {\text { C. } x^{2}-1} & {\text { D. } x-1}\end{array}\)

What is the expanded form of \((a-b)^{3} ?\) \(\begin{array}{ll}{\text { A. } a^{3}+a^{2} b+a b^{2}+b^{3}} & {\text { B. } a^{3}+3 a^{2} b+3 a b^{2}+b^{3}} \\ {\text { C. } a^{3}-a^{2} b+a b^{2}-b^{3}} & {\text { D. } a^{3}-3 a^{2} b+3 a b^{2}-b^{3}}\end{array}\)

What is the polynomial function, in standard form, whose zeros are \(-2,5,\) and \(6,\) and whose leading coefficient is \(-2 ?\) Justify your reasoning.

Which term in the expansion of \((2 a-3 b)^{6}\) has coefficient 2160\(?\) \(\begin{array}{ll}{\text { F. second term }} & {\text { G. third term }} \\\ {\text { H. fourth term }} & {\text { J. fifth term }}\end{array}\)