Chapter 3

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ x^{3}-5 x^{2}+17 x-13-0 $$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$ f(x)=11 x^{3}-6 x^{2}+x+3 $$

Divide using synthetic division. $$ \left(5 x^{2}-12 x-8\right) \div(x+3) $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$f(x)-(x-3)^{2}+2$$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 2 x^{2}+3 x>0 $$

Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, of the graph of each rational function. $$f(x)=\frac{x}{x+4}$$

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ 6 x^{3}+25 x^{2}-24 x+5-0 $$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$ f(x)=5 x^{4}+7 x^{2}-x+9 $$

Divide using synthetic division. $$ \left(4 x^{3}-3 x^{2}+3 x-1\right) \div(x-1) $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$y-1-(x-3)^{2}$$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 3 x^{2}-5 x \leq 0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. An object's weight on the moon, \(M,\) varies directly as its weight on Earth, \(E .\) Neil Armstrong, the first person to step on the moon on July \(20,1969,\) weighed 360 pounds on Earth (with all of his equipment on) and 60 pounds on the moon. What is the moon weight of a person who weighs 186 pounds on Earth?

Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, of the graph of each rational function. $$f(x)=\frac{x}{x-3}$$

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ 2 x^{3}-5 x^{2}-6 x+4=0 $$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$ f(x)=11 x^{4}-6 x^{2}+x+3 $$

Divide using synthetic division. $$ \left(5 x^{3}-6 x^{2}+3 x+11\right) \div(x-2) $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$y-3-(x-1)^{2}$$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ -x^{2}+x \geq 0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. The height that a ball bounces varies directly as the height from which it was dropped. A tennis ball dropped from 12 inches bounces 8.4 inches. From what height was the tennis ball dropped if it bounces 56 inches?

Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, of the graph of each rational function. $$g(x)=\frac{x+3}{x(x+4)}$$

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ x^{4}-2 x^{3}-5 x^{2}+8 x+4-0 $$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$ f(x)=5 x^{4}+7 x^{2}-x+9 $$

Divide using synthetic division. $$ \left(6 x^{5}-2 x^{3}+4 x^{2}-3 x+1\right) \div(x-2) $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$f(x)-2(x+2)^{2}-1$$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ -x^{2}+2 x \geq 0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. The distance that a spring will stretch varies directly as the force applied to the spring. A force of 12 pounds is needed to stretch a spring 9 inches. What force is required to stretch the spring 15 inches?

Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, of the graph of each rational function. $$g(x)=\frac{x+3}{x(x-3)}$$

In Exercises \(17-24\) a. List all possible rational roots. b. Use synthetic division to test the possible rational roots and find an actual root. c. Use the quotient from part (b) to find the remaining roots and solve the equation. $$ x^{4}-2 x^{2}-16 x-15-0 $$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $$ f(x)=11 x^{4}-6 x^{2}+x+3 $$

Divide using synthetic division. $$ \left(x^{5}+4 x^{4}-3 x^{2}+2 x+3\right) \div(x-3) $$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2} \leq 4 x-2 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. If all men had identical body types, their weight would vary directly as the cube of their height. Shown below is Robert Wadlow, who reached a record height of 8 feet 11 inches \((107 \text { inches ) before his death at age } 22 .\) If a man who is 5 feet 10 inches tall \((70\) inches) with the same body type as Mr. Wadlow weighs 170 pounds, what was Robert Wadlow's weight shortly before his death?

Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, of the graph of each rational function. $$h(x)=\frac{x}{x(x+4)}$$

Find the zeros for each polynomial function and give the multiplicity for each zera. State whether the graph crosses the \(x\) -axis, or touches the \(x\) -axis and turns around, at each zera $$ f(x)=2(x-5)(x+4)^{2} $$

Divide using synthetic division. $$ \left(x^{2}-5 x-5 x^{3}+x^{4}\right) \div(5+x) $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$f(x)-4-(x-1)^{2}$$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ x^{2} \leq 2 x+2 $$

Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, of the graph of each rational function. $$h(x)=\frac{x}{x(x-3)}$$

Find the zeros for each polynomial function and give the multiplicity for each zera. State whether the graph crosses the \(x\) -axis, or touches the \(x\) -axis and turns around, at each zera $$ f(x)=3(x+5)(x+2)^{2} $$

Divide using synthetic division. $$ \left(x^{2}-6 x-6 x^{3}+x^{4}\right) \div(6+x) $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$f(x)-1-(x-3)^{2}$$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 9 x^{2}-6 x+1<0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. The figure shows that a bicyclist tips the cycle when making a turn. The angle \(\vec{B},\) formed by the vertical direction and the bicycle, is called the banking angle. The banking angle varies inversely as the cycle's turning radius. When the turning radius is 4 feet, the banking angle is \(28^{\circ} .\) What is the banking angle when the turning radius is 3.5 feet?

Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, of the graph of each rational function. $$r(x)=\frac{x}{x^{2}+4}$$

Find the zeros for each polynomial function and give the multiplicity for each zera. State whether the graph crosses the \(x\) -axis, or touches the \(x\) -axis and turns around, at each zera $$ f(x)=4(x-3)(x+6)^{3} $$

Divide using synthetic division. $$ \frac{x^{5}+x^{3}-2}{x-1} $$

Use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the function's domain and range. $$f(x)-x^{2}-2 x-3$$

Solve each polynomial inequality in Exercises \(1-42\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 4 x^{2}-4 x+1 \geq 0 $$

Use the four-step procedure for solving variation problems given on page 424 to solve. The water temperature of the Pacific Ocean varies inversely as the water's depth. At a depth of 1000 meters, the water temperature is \(4.4^{\circ}\) Celsius. What is the water temperature at a depth of 5000 meters?

Find the vertical asymptotes, if any, and the values of \(x\) corresponding to holes, if any, of the graph of each rational function. $$r(x)=\frac{x}{x^{2}+3}$$