91Ó°ÊÓ

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies directly as \(x . y=45\) when \(x=5 .\) Find \(y\) when \(x=13 .\)

Divide using long division. State the quotient, q(x), and the remainder, r(x). $$\left(x^{3}+5 x^{2}+7 x+2\right) \div(x+2)$$

Use the four-step procedure for solving variation problems given on page 424 to solve. \(a\) varies directly as \(b\) and inversely as the square of \(c . a=7\) when \(b=9\) and \(c=6 .\) Find \(a\) when \(b=4\) and \(c=8\).

Write an equation that expresses each relationship. Then solve the equation for \(y .\) \(x\) varies directly as the cube root of \(z\) and inversely as \(y .\)

Solve each polynomial inequality and graph the solution set on a real number line. Express each solution set in interval notation. $$ 3 x^{2}+16 x<-5 $$

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. $$x^{3}-2 x^{2}-11 x+12=0$$

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

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

Find an nuth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. \(n=3 ; 4\) and \(2 i\) are zeros; \(f(-1)=-50\)

The illumination provided by a car's headlight varies inversely as the square of the distance from the headlight. A car's headlight produces an illumination of 3.75 footcandles at a distance of 40 feet. What is the illumination when the distance is 50 feet?