Polynomial Functions and Inequalities

The video tutorial explains how to solve polynomial inequalities by finding zeros, plotting them on a number line, and testing intervals to determine which satisfy the inequality. It covers factoring by grouping, evaluating test values, and graphically verifying solutions. The solution is expressed using both interval notation and inequalities.

What is the first step in solving a polynomial inequality?

• Testing values in each interval

• Expressing the solution in interval notation

• Graphing the polynomial

• Finding the zeros of the polynomial

Which method is used to find the zeros of the polynomial X^3 - 6X^2 - 4X + 24?

• Using the quadratic formula

• Factoring by grouping

• Synthetic division

• Completing the square

How are zeros plotted on a number line when the inequality is strictly less than?

• As shaded regions

• As arrows

• As open points

• As closed points

What is the purpose of choosing test values in each interval?

• To determine if the interval satisfies the inequality

• To calculate the derivative

• To simplify the polynomial

• To find the maximum value of the polynomial

Which test value results in a true statement for the interval to the left of -2?

• x = 0

• x = 3

• x = -3

• x = 7

What is the result of evaluating the polynomial at x = 0?

• -45

• 24

• -24

• 0

Which interval is part of the solution when x = 3 is tested?

• x > 2 and x < 6

• x = 0

• x < -2

• x > 6

How is the solution expressed using interval notation for x < -2?

• (2, 6)

• (-∞, -2]

• (-∞, -2)

• [-2, ∞)

What does it mean graphically when the polynomial is less than zero?

• The graph is tangent to the x-axis

• The graph is below the x-axis

• The graph is above the x-axis

• The graph is on the x-axis

What is the correct interval notation for the solution where x is greater than 2 and less than 6?

• [2, 6]

• [2, 6)

• (2, 6]

• (2, 6)