91Ó°ÊÓ

In Exercises 65 - 74, find a polynomial of degree \( n \) that has the given zero(s). (There are many correct answers.) Zero(s) Degree \( x = -5, 0, 1 \), \( n = 3 \)

In Exercises 67 - 74, (a) verify the given factors of the function \( f \),(b) find the remaining factor(s) of \( f \) (c) use your results to write the complete factorization of \( f \), (d) list all real zeros of \( f \), and (e) confirm your results by using a graphing utility to graph the function. Function Factors \( f(x) = 3x^3 + 2x^2 - 19x + 6 \) \( (x + 3) \), \( (x - 2) \)

In Exercises 65 - 70, solve the inequality. (Round your answers to two decimal places.) \( \dfrac{1}{2.3x - 5.2} > 3.4 \)

The revenue and cost equations for a product are \( R = x(75 - 0.0005x) \) and \( C = 30x + 250,000, \) where \( R \) and \( C \) e measured in dollars and \( x \) represents the number of units sold.How many units must be sold to obtain a profit of at least \( \$750,000 \)? What is the price per unit?

The revenue and cost equations for a product are \( R = x(50 - 0.0002x) \) and \( C = 12x + 150,000, \) where \( R \) and \( C \) are measured in dollars and \( x \) represents the number of units sold. How many units must be sold to obtain a profit of at least \( \$1,650,000 \)? What is the price per unit?

In Exercises 75 - 80, (a) use the zero or root feature of a graphing utility to approximate the zeros of the function accurate to three decimal places,(b) determine one of the exact zeros, and (c) use synthetic division to verify your result from part (b), and then factor the polynomial completely. \( h(t) = t^3 - 2t^2 - 7t + 2 \)

The cost \( C \) (in millions of dollars) of removing \( p\% \) of the industrial and municipal pollutants discharged into a river is given by \( C = \dfrac{255p}{100 - p}, 0 \le p \le 100 \). (a) Use a graphing utility to graph the cost function. (b) Find the costs of removing \( 10\% \), \( 40\% \), and \( 75\% \) of the pollutants. (c) According to this model, would it be possible to remove \( 100\% \) of the pollutants? Explain.

In Exercises 75 - 88, sketch the graph of the function by (a) applying the Leading Coefficient Test, (b) finding the zeros of the polynomial, (c) plotting sufficient solution points, and(d) drawing a continuous curve through the points. \( g(x) = -x^2 + 10x - 16 \)

In Exercises 75 - 88, sketch the graph of the function by (a) applying the Leading Coefficient Test, (b) finding the zeros of the polynomial, (c) plotting sufficient solution points, and(d) drawing a continuous curve through the points. \( f(x) = 8 - x^3 \)

In Exercises 81 - 84, simplify the rational expression by using long division or synthetic division. \( \frac{4x^3 - 8x^2 + x + 3}{2x - 3} \)