Chapter 6

ACT/SAT The measure of the largest angle of a triangle is 14 less than twice the measure of the smallest angle. The third angle is 2 more than the measure of the smallest angle. What is the measure of the smallest angle? \(\begin{array}{rllllll}{\mathbf{F}} & {46} & {\mathbf{G} 48} & {\mathrm{H} 50} & {\mathbf{J}} & {82}\end{array}\)

Simplify. Assume that no variable equals \(0 .\) $$ \frac{x^{2} y z^{4}}{x y^{3} z^{2}} $$

Find the greatest common factor of each set of numbers. $$ 24,84 $$

Find all values of \(\pm \frac{a}{b}\) given each replacement set. \(a=\\{1,2,4\\} ; b=\\{1,2,4,8,16\\}\)

Simplify. \(\frac{3 x^{4}+x^{3}-8 x^{2}+10 x-3}{3 x-2}\)

REVIEW \(27 x^{3}+y^{3}=\) \(\mathbf{A}(3 x+y)(3 x+y)(3 x+y)\) \(\mathbf{B}(3 x+y)\left(9 x^{2}-3 x y+y^{2}\right)\) \(\mathbf{C}(3 x-y)\left(9 x^{2}+3 x y+y^{2}\right)\) \(\mathbf{D}(3 x-y)\left(9 x^{2}+9 x y+y^{2}\right)\)

Simplify. Assume that no variable equals \(0 .\) $$ \left(\frac{3 a b^{2}}{6 a^{2} b}\right)^{2} $$

Find the greatest common factor of each set of numbers. $$ 16,28 $$

Ms. Schifflet is writing a computer program to find the salaries of her employees after their annual raise. The percent of increase is represented by \(p\) . Marty's salary is \(\$ 23,450\) now. Write a polynomial to represent Marty's salary in one year and another to represent Marty's salary after three years. Assume that the rate of increase will be the same for each of the three years.

Graph each polynomial function. Estimate the \(x\) -coordinates at which the relative maxima and relative minima occur. $$ f(x)=x^{3}-6 x^{2}+4 x+3 $$

Graph each inequality. $$ y>x^{2}-4 x+6 $$

Find the greatest common factor of each set of numbers. $$ 12,27,48 $$

Solve each equation by completing the square. \(x^{2}-8 x-2=0\)

Graph each polynomial function. Estimate the \(x\) -coordinates at which the relative maxima and relative minima occur. $$ f(x)=-x^{4}+2 x^{3}+3 x^{2}-7 x+4 $$

Graph each inequality. $$ y \leq-x^{2}+6 x-3 $$

Find the greatest common factor of each set of numbers. $$ 12,30,54 $$

Solve each equation by completing the square. \(x^{2}+\frac{1}{3} x-\frac{35}{36}=0\)

Find \(p(7)\) and \(p(-3)\) for each function. $$ p(x)=x^{2}-5 x+3 $$

Graph each inequality. $$ y

Solve each equation. $$ 2 x+11=25 $$

Find the greatest common factor of each set of numbers. $$ 15,30,65 $$

Find \(p(7)\) and \(p(-3)\) for each function. $$ p(x)=x^{3}-11 x-4 $$

Determine whether each function has a maximum or a minimum value. Then find the maximum or minimum value of each function. $$ f(x)=x^{2}-8 x+3 $$

Solve each equation. $$ -12-5 x=3 $$

Find \(p(7)\) and \(p(-3)\) for each function. $$ p(x)=\frac{2}{3} x^{4}-3 x^{3} $$

Determine whether each function has a maximum or a minimum value. Then find the maximum or minimum value of each function. $$ f(x)=-3 x^{2}-18 x+5 $$

PREREQUISITE SKILL. Use the Distributive Property to find each product. $$ 2(x+y) $$

PHOTOGRAPHY. The perimeter of a rectangular picture is 86 inches. Twice the width exceeds the length by 2 inches. What are the dimensions of the picture?

Determine whether each function has a maximum or a minimum value. Then find the maximum or minimum value of each function. $$ f(x)=-7+4 x^{2} $$

PREREQUISITE SKILL. Use the Distributive Property to find each product. $$ 3(x-z) $$

PREREQUISITE SKILL. Use the Distributive Property to find each product. $$ 4(x+2) $$

Name the property illustrated by each statement. If \(3 x=4 y\) and \(4 y=15 z,\) then \(3 x=15 z\)

PREREQUISITE SKILL. Use the Distributive Property to find each product. $$ -2(3 x-5) $$

Name the property illustrated by each statement. \(5 y(4 a-6 b)=20 a y-30 b y\)

PREREQUISITE SKILL Find each quotient. $$ \left(x^{3}+4 x^{2}-9 x+4\right) \div(x-1) $$

Use matrices \(A, B, C,\) and \(D\) to find the following. $$ A=\left[\begin{array}{rr}{-4} & {4} \\ {2} & {-3} \\ {1} & {5}\end{array}\right] \quad B=\left[\begin{array}{rr}{7} & {0} \\ {4} & {1} \\\ {6} & {-2}\end{array}\right] \quad C=\left[\begin{array}{rr}{-4} & {-5} \\\ {-3} & {1} \\ {2} & {3}\end{array}\right] \quad D=\left[\begin{array}{rr}{1} & {-2} \\ {1} & {-1} \\ {-3} & {4}\end{array}\right] $$ $$ 3 B-2 A $$

PREREQUISITE SKILL. Use the Distributive Property to find each product. $$ -5(x-2 y) $$

Name the property illustrated by each statement. \(2+(3+x)=(2+3)+x\)

PREREQUISITE SKILL Find each quotient. $$ \left(4 x^{3}-8 x^{2}-5 x-10\right) \div(x+2) $$

PREREQUISITE SKILL. Use the Distributive Property to find each product. $$ -3(-y+5) $$

Graph each equation by making a table of values. \(y=x^{2}+4\)

PREREQUISITE SKILL Find each quotient. $$ \left(x^{4}-9 x^{2}-2 x+6\right) \div(x-3) $$

Graph each equation by making a table of values. \(y=-x^{2}+6 x-5\)

PREREQUISITE SKILL Find each quotient. $$ \left(x^{4}+3 x^{3}-8 x^{2}+5 x-6\right) \div(x+1) $$

In \(1990,2,573,225\) people attended St. Louis Cardinals home games. In 2004 , the attendance was \(3,048,427 .\) What was the average annual rate of increase in attendance?

Graph each equation by making a table of values. \(y=\frac{1}{2} x^{2}+2 x-6\)

PREREQUISITE SKILL. Simplify. Assume that no variable equals 0. $$ \frac{x^{3}}{x} $$

PREREQUISITE SKILL. Simplify. Assume that no variable equals 0. $$ \frac{4 y^{5}}{2 y^{2}} $$

PREREQUISITE SKILL. Simplify. Assume that no variable equals 0. $$ \frac{x^{2} y^{3}}{x y} $$

PREREQUISITE SKILL. Simplify. Assume that no variable equals 0. $$ \frac{9 a^{3} b}{3 a b} $$