Chapter 1

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$3 x^{4}-48 x^{2}=0$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ (1,6] $$

Solve equation by factoring. $$ x^{2}-3 x-10=0 $$

According to the American Bureau of Labor Statistics, you will devote 37 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 19. Over your lifetime, how many years will you spend on each of these activities?

Add or subtract as indicated and write the result in standard form. $$ (7+2 i)+(1-4 i) $$

Solve and check each linear equation. $$7 x-5=72$$

In Exercises 1–12, plot the given point in a rectangular coordinate system. $$(1,4)$$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$5 x^{4}-20 x^{2}=0$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ (-2,4] $$

Solve equation by factoring. $$ x^{2}-13 x+36=0 $$

According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. Over your lifetime, how many years will you spend on each of these activities?

Add or subtract as indicated and write the result in standard form. $$ (-2+6 i)+(4-i) $$

Solve and check each linear equation. $$6 x-3=63$$

In Exercises 1–12, plot the given point in a rectangular coordinate system. $$(2,5)$$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$3 x^{3}+2 x^{2}=12 x+8$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ [-5,2) $$

Solve equation by factoring. $$ x^{2}=8 x-15 $$

The median yearly salary of an American whose final degree is a master's is \(\$ 70\) thousand less than twice that of an American whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn \(\$ 173\) thousand. Find the median yearly salary of Americans with each of these final degrees.

Add or subtract as indicated and write the result in standard form. $$ (3+2 i)-(5-7 i) $$

Solve and check each linear equation. $$11 x-(6 x-5)=40$$

In Exercises 1–12, plot the given point in a rectangular coordinate system. $$(-2,3)$$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$4 x^{3}-12 x^{2}=9 x-27$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ [-4,3) $$

Solve equation by factoring. $$ x^{2}=-11 x-10 $$

The median yearly salary of an American whose final degree is a doctorate is \(\$ 45\) thousand less than twice that of an American whose final degree is a bachelor's. Combined, two people with each of these educational attainments earn \(\$ 198\) thousand. Find the median yearly salary of Americans with each of these final degrees.

Solve and check each linear equation. $$5 x-(2 x-10)=35$$

Add or subtract as indicated and write the result in standard form. $$ (-7+5 i)-(-9-11 i) $$

In Exercises 1–12, plot the given point in a rectangular coordinate system. $$(-1,4)$$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$2 x-3=8 x^{3}-12 x^{2}$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ [-3,1] $$

Solve equation by factoring. $$ 6 x^{2}+11 x-10=0 $$

In \(2014,\) the average price of a new car was \(\$ 37,600 .\) For the period shown, new-car prices increased by approximately \(\$ 1250\) per year. If this trend continues, how many years after 2014 will the price of a new car average \(\$ 46,350 ?\) In which year will this occur?

Solve and check each linear equation. $$2 x-7=6+x$$

Add or subtract as indicated and write the result in standard form. $$ 6-(-5+4 i)-(-13-i) $$

In Exercises 1–12, plot the given point in a rectangular coordinate system. $$(-3,-5)$$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$x+1=9 x^{3}+9 x^{2}$$

Solve equation by factoring. $$ 9 x^{2}+9 x+2=0 $$

In 2014, the average age of cars on U.S. roads was 11.3 years. For the period shown, this average age increased by approximately 0.2 year per year. If this trend continues, how many years after 2014 will the average age of vehicles on U.S. roads be 12.3 years? In which year will this occur?

Solve and check each linear equation. $$3 x+5=2 x+13$$

Add or subtract as indicated and write the result in standard form. $$ 7-(-9+2 i)-(-17-i) $$

In Exercises 1–12, plot the given point in a rectangular coordinate system. $$(-4,-2)$$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$4 y^{3}-2=y-8 y^{2}$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ (2, \infty) $$

Solve equation by factoring. $$ 3 x^{2}-2 x=8 $$

A new car worth \(\$ 24,000\) is depreciating in value by \(\$ 3000\) per year. a. Write a formula that models the car's value, \(y,\) in dollars, after \(x\) years. b. Use the formula from part (a) to determine after how many years the car's value will be \(\$ 9000\). c. Graph the formula from part (a) in the first quadrant of a rectangular coordinate system. Then show your solution to part (b) on the graph.

Solve and check each linear equation. $$7 x+4=x+16$$

Add or subtract as indicated and write the result in standard form. $$ 8 i-(14-9 i) $$

In Exercises 1–12, plot the given point in a rectangular coordinate system. $$ (4,-1) $$

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. $$9 y^{3}+8=4 y+18 y^{2}$$

In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. $$ (3, \infty) $$