Question

A. When solving a polynomial inequality by hand, the solutions of the associated equation are called the______ numbers. These numbers divide up the number line into regions that contain or do not contain_____of the inequality.

b. When solving a rational inequality by hand, the solutions of the associated equation as well as values that make the________ of the rational expression zero are called the________ numbers. The restriction of a rational expression is________ included in the solution set.

Answer 1

Critical numbers are the solutions to the associated equation in a polynomial inequality, which divided the number line into regions with or without solutions. For rational inequalities, they also include values that make the denominator zero, which are not part of the solution set.

Step-by-step explanation:

When solving a polynomial inequality by hand, the solutions of the associated equation are called the critical numbers. These numbers divide up the number line into regions that contain or do not contain solutions of the inequality.

When solving a rational inequality by hand, the solutions of the associated equation as well as values that make the denominator of the rational expression zero are called the critical numbers. The restriction of a rational expression is never included in the solution set.

Answer 2

Answer: A. boundary, solutions B. denominator, boundary, not

Step-by-step explanation:

A. When solving a polynomial inequality by hand, the solutions of the associated equation are called the boundary numbers. These numbers divide up the number line into regions that contain or do not contain solutions of the inequality.

B. When solving a rational inequality by hand, the solutions of the associated equation as well as values that make the denominator of the rational expression zero are called the boundary numbers. The restriction of a rational expression is not included in the solution set.

This is the correct (Tophat) version