Chapter 6

Solve each equation by graphing. Check your answers. $$ 4 x^{3}=4 x^{2}+3 x $$

Divide using long division. Check your answers. $$ \left(x^{2}-7 x+10\right) \div(x+3) $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ -x^{5} $$

Use Pascal's Triangle to expand each binomial. $$ (d+1)^{9} $$

Evaluate each expression. $$ \frac{15 !}{10 ! 5 !} $$

For each equation, state the number of complex roots, the possible number of real roots, and the possible rational roots. $$ x^{10}+x^{8}-x^{4}+3 x^{2}-x+1=0 $$

Write each polynomial in factored form. Check by multiplication. $$ 9 x^{3}+6 x^{2}-3 x $$

Find the roots of each polynomial equation. $$ x^{3}-5 x^{2}+7 x-35=0 $$

Solve each equation by graphing. Check your answers. $$ 2 x^{4}-5 x^{3}-3 x^{2}=0 $$

Divide using long division. Check your answers. $$ \left(x^{3}-13 x-12\right) \div(x-4) $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ 3+12 x^{4} $$

Use Pascal's Triangle to expand each binomial. $$ (x-3)^{3} $$

Automobiles You should rotate tires on a car at regular intervals. a. In how many ways can four tires be arranged on a car? b. If the spare tire is included, how many arrangements are possible?

Find all the zeros of each function. $$ y=2 x^{3}+x^{2}+1 $$

Write each polynomial in factored form. Check by multiplication. $$ 10 x^{3}-10 x^{2}+15 x $$

Find the roots of each polynomial equation. $$ 2 x^{4}-5 x^{3}-17 x^{2}+41 x-21=0 $$

Solve each equation by graphing. Check your answers. $$ x^{2}-8 x+7=0 $$

Determine whether each binomial is a factor of \(x^{3}+4 x^{2}+x-6\) $$x+1$$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ 6 x^{3}-x^{3} $$

Use Pascal's Triangle to expand each binomial. $$ (a+3 b)^{4} $$

Find all the zeros of each function. $$ f(x)=x^{3}-3 x^{2}+x-3 $$

Write each polynomial in factored form. Check by multiplication. $$ x^{3}+7 x^{2}+10 x $$

Find the roots of each polynomial equation. $$ 4 x^{3}+16 x^{2}-22 x-10=0 $$

Savings The polynomial \(1600 x^{3}+1200 x^{2}+800 x\) represents your savings,with interest, from a summer ob after three years. The annual interest rate equals \(x-1 .\) Find the interest rate needed so that you will have \(\$ 4000\) at the end of three years.

Determine whether each binomial is a factor of \(x^{3}+4 x^{2}+x-6\) $$ x+2 $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ 7 x^{3}-10 x^{3}+x^{3} $$

Use Pascal's Triangle to expand each binomial. $$ (x-2)^{6} $$

Evaluate each expression. \(_{8} P_{2}\)

Find all the zeros of each function. $$ g(x)=x^{3}-5 x^{2}+5 x-4 $$

Write each polynomial in factored form. Check by multiplication. $$ x^{3}+8 x^{2}+16 x $$

Find the roots of each polynomial equation. $$ 4 x^{4}-37 x^{2}+9=0 $$

Geometry The volume \(V\) of a container is modeled by the function \(V(x)=x^{3}-3 x^{2}-4 x \cdot\) Let \(x, x+1,\) and \(x-4\) represent the width, the length, and the height respectively. The container has a volume of 70 \(\mathrm{ft}^{3}\) . Find the container's dimensions.

Determine whether each binomial is a factor of \(x^{3}+4 x^{2}+x-6\) $$ x+3 $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ 4 x+5 x^{2}+8 $$

Use Pascal's Triangle to expand each binomial. $$ (x-4)^{8} $$

Evaluate each expression. \(_{8} P_{3}\)

Find all the zeros of each function. $$ y=x^{3}-2 x^{2}-3 x+6 $$

Write each polynomial in factored form. Check by multiplication. $$ x^{3}-7 x^{2}-18 x $$

Find the roots of each polynomial equation. $$ 9 x^{4}+3 x^{3}-30 x^{2}+6 x+12=0 $$

Determine whether each binomial is a factor of \(x^{3}+4 x^{2}+x-6\) $$ x-3 $$

Write each polynomial in standard form. Then classify it by degree and by number of terms. $$ x^{2}-x^{4}+2 x^{2} $$

Use the Binomial Theorem to expand each binomial. $$(x+y)^{4}$$

Evaluate each expression. \(_{8} P_{4}\)

Find all the zeros of each function. $$ y=x^{4}-6 x^{2}+8 $$

Find the relative maximum, relative minimum, and zeros of each function. $$ f(x)=x^{3}+4 x^{2}-5 x $$

A polynomial equation with rational coefficients has the given roots. Find two additional roots. $$ \sqrt{5} \text { and }-\sqrt{13} $$

Factor each expression. $$ x^{3}-1000 $$

Divide using synthetic division. $$ \left(x^{3}+3 x^{2}-x-3\right) \div(x-1) $$

Use the Binomial Theorem to expand each binomial. $$ (w+1)^{5} $$

Evaluate each expression. \(_{3} \mathrm{P}_{2}\)