Polynomial Inequalities Answers

What is the solution to (x – 5)(2x + 1)(x – 7) > 0?

An aquarium has dimensions 2x feet, (x – 1) feet, and (x + 2) feet. The aquarium volume must be no more than 280 cubic feet.What are the possible values of x?

The cube of a number is less than five times the square of the number. For what set of numbers is this true?

Consider the graph of f(x) = 2x 3 – 3x 2 – 14x.

You are building a rectangular garden against the back of your house, using 80 feet of fencing. The area of the garden needs to be greater than 400 square feet but less than 600 square feet.

What are the minimum and maximum values of x, for which x3 + x2 – 6x ≥ 0?

The width of a rectangular prism is five less than the length, and the height of the prism is twice the length. Let x represent the length of the prism.For what values of x will the volume of the rectangular prism be 500 cubic units or greater?

What is the solution to x6 – 6x 5 + 15x 4 – 20x 3 + 15x 2 – 6x + 1 ≥ 0?

The graph of f(x) = (0.2)(x4 + x3 – 12x2) is shown.

A ski lift is modeled by the function f(x) = (0.2)(–2x 3 + 23x 2 + 25x + 50), where x is the time in seconds. When it comes out of the first stop, it is now climbing toward its highest point from the ground.During which time interval will the ski lift reach a height over 50 feet above the ground?