Solving Polynomial Inequalities with Sign Charts

This video tutorial focuses on solving polynomial inequalities. It begins with an introduction to the concept, explaining the difference between equations and inequalities. The tutorial then provides a step-by-step guide to solving quadratic inequalities using number lines and interval notation. It includes examples of both quadratic and cubic polynomial inequalities, demonstrating techniques such as factoring, the rational zero theorem, and synthetic division. The video concludes with advanced examples, ensuring a comprehensive understanding of solving polynomial inequalities.

What is the first step in solving a polynomial inequality?

• Test the regions

• Create a number line

• Factor the polynomial

• Move all terms to one side of the inequality

Which two numbers multiply to -10 and add to 3 in the inequality x^2 + 3x > 10?

• 5 and -2

• 2 and -5

• 4 and -1

• 1 and -4

What type of circle is used on the number line for points that are not included in the solution?

• Filled circle

• Dotted circle

• Open circle

• Closed circle

In the inequality x^2 + 3x > 10, which regions on the number line are part of the solution?

• Between -2 and 5

• Less than -2 and greater than 5

• Less than -5 and greater than 2

• Between -5 and 2

What is the standard form of the inequality x^3 - x ≤ 3x^2 - 3?

• x^3 - 3x^2 + x - 3 ≤ 0

• x^3 - 3x^2 - x + 3 ≤ 0

• x^3 - x^2 - 3x + 3 ≤ 0

• x^3 + 3x^2 - x - 3 ≤ 0

What is the greatest common factor (GCF) of the first two terms in the expression x^3 - 3x^2 - x + 3?

• 3

• 1

• x^2

• x

Which points are included in the solution for the inequality x^3 - x ≤ 3x^2 - 3?

• -2, 2, and 3

• -2, 1, and 3

• -1, 2, and 3

• -1, 1, and 3

What is the first step in solving the inequality x^3 - 2x^2 ≥ 5x - 6?

• Move all terms to one side

• Factor by grouping

• Use the rational zero theorem

• Create a number line

Which of the following is a factor of the polynomial x^3 - 2x^2 - 5x + 6?

• x + 2

• x - 2

• x + 1

• x - 1

What is the interval notation for the solution of the inequality x^3 - 2x^2 ≥ 5x - 6?

• (-∞, -2] ∪ [1, 3]

• (-∞, -2) ∪ (1, 3)

• (-2, 1) ∪ (3, ∞)

• [-2, 1] ∪ [3, ∞)