Polynomial Inequalities and Graphing Concepts

The video tutorial explains how to solve a polynomial inequality given in factored form. It involves finding x-values that make the product zero, forming intervals on a number line, and testing each interval to see if it satisfies the inequality. The solution is verified graphically by analyzing when the function is on or above the x-axis.

What is the first step in solving a polynomial inequality?

• Graph the inequality

• Find the derivative

• Integrate the function

• Set the inequality to zero and solve for x

When does the factor 'x plus two' equal zero?

• When x equals -2

• When x equals 0

• When x equals 3

• When x equals 2

How many intervals are formed on the number line after plotting the critical points?

• One

• Two

• Three

• Four

Which test value is used for the interval on the left?

• x equals 3

• x equals -3

• x equals 4

• x equals 0

What is the result of substituting x equals 0 into the inequality?

• The inequality is undefined

• The inequality is false

• The inequality is zero

• The inequality is true

Which interval is part of the solution after testing x equals 4?

• Interval on the left

• Interval in the middle

• Interval on the right

• None of the intervals

What x-values satisfy the inequality according to the graph?

• x equals -2 and x greater than or equal to 3

• x equals -2 and x less than 3

• x equals 2 and x greater than 3

• x equals 2 and x less than or equal to 3

What does the graph indicate about the function at x equals -2?

• The function is below the x-axis

• The function touches the x-axis

• The function is above the x-axis

• The function is undefined

What is a benefit of solving polynomial inequalities graphically?

• It provides a visual verification of the solution

• It is faster than algebraic methods

• It eliminates the need for calculations

• It is the only method to solve inequalities

What does the graph verify about the solution?

• The solution is incorrect

• The solution is partially correct

• The solution is correct

• The solution is undefined