Polynomial Inequalities and Interval Notation

The video tutorial explains how to solve polynomial inequalities by finding zeros through factoring, plotting them on a number line, and testing intervals to determine which parts satisfy the inequality. It also covers expressing solutions using inequalities and interval notation, and verifies the solution graphically.

What is the first step in solving a polynomial inequality?

• Testing values in intervals

• Finding the zeros of the polynomial

• Graphing the polynomial

• Expressing the solution in interval notation

Which method is used to solve the equation 2x^3 - 5x^2 - 12x = 0?

• Completing the square

• Graphing

• Using the quadratic formula

• Factoring

What do closed points on a number line indicate in the context of inequalities?

• The values are excluded from the solution

• The values are approximate

• The values are part of the solution

• The values are not part of the solution

How many intervals are created by the points -3/2, 0, and 4 on the number line?

• Five

• Four

• Three

• Two

What is the result of evaluating the inequality at x = -3?

• False, but the interval is part of the solution

• False, the interval is not part of the solution

• True, the interval is part of the solution

• True, but the interval is not part of the solution

Which test value confirms that the interval between -3/2 and 0 is part of the solution?

• x = 5

• x = -1

• x = 1

• x = -3

What is the interval notation for the solution where x is greater than or equal to 4?

• (-∞, 4]

• [4, ∞)

• (4, ∞)

• [4, 5]

How is the solution verified graphically?

• By checking if the graph is above or on the x-axis

• By checking if the graph is parallel to the x-axis

• By checking if the graph intersects the y-axis

• By checking if the graph is below the x-axis

What does the inequality symbol 'greater than or equal to' imply about the solution?

• The solution includes the points where the polynomial is zero

• The solution excludes the points where the polynomial is zero

• The solution is only valid for positive x values

• The solution is only valid for negative x values

What is the interval notation for the solution between -3/2 and 0?

• (-3/2, 0)

• [-3/2, 0]

• (-3/2, 0]

• [-3/2, 0)