CCP Ch 8 - Solve Polynomial Inequalities

Front

What is a polynomial inequality?

Back

A polynomial inequality is an inequality that involves a polynomial expression, typically in the form of f(x) > 0, f(x) < 0, f(x) ≥ 0, or f(x) ≤ 0.

Front

How do you solve a polynomial inequality?

Back

To solve a polynomial inequality, first solve the corresponding polynomial equation to find critical points, then test intervals between these points to determine where the inequality holds true.

Front

What are critical points in polynomial inequalities?

Back

Critical points are the values of x where the polynomial equals zero or is undefined, which are used to divide the number line into intervals for testing.

Front

What does the notation (a, b) represent in interval notation?

Back

The notation (a, b) represents an open interval, meaning it includes all numbers between a and b, but not a and b themselves.

Front

What does the notation [a, b] represent in interval notation?

Back

The notation [a, b] represents a closed interval, meaning it includes all numbers between a and b, including a and b.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints, while closed intervals do include their endpoints.

Front

How do you determine where a polynomial is positive?

Back

To determine where a polynomial is positive, find the intervals where the polynomial is above the x-axis by testing values in each interval created by the critical points.

Front

What is the significance of the union symbol (U) in interval notation?

Back

The union symbol (U) is used to combine two or more intervals, indicating that the solution includes all values from each interval.

Front

What does it mean for a polynomial to be greater than zero?

Back

A polynomial being greater than zero means that the values of the polynomial function are positive for certain intervals of x.

Front

What is the solution to the inequality f(x) > 0 if f(x) has roots at -4, -1, and 2?

Back

The solution is (-4, -1) U (2, +∞), meaning the polynomial is positive in these intervals.