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 find the roots of the corresponding polynomial equation, then test intervals between the roots to determine where the inequality holds true.

Front

What does it mean for f(x) > 0?

Back

It means that the values of the function f(x) are positive, indicating that the graph of the polynomial is above the x-axis.

Front

What is the significance of the roots in polynomial inequalities?

Back

The roots of the polynomial are the points where the function intersects the x-axis, and they help to divide the number line into intervals for testing the sign of the polynomial.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line, using parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the notation (-4, -1) U (2, +∞) represent?

Back

It represents the union of two intervals: all numbers between -4 and -1 (not including -4 and -1) and all numbers greater than 2.

Front

How do you determine the sign of a polynomial in an interval?

Back

Choose a test point from the interval and substitute it into the polynomial. If the result is positive, the polynomial is positive in that interval; if negative, it is negative.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

Front

What is the role of the leading coefficient in polynomial inequalities?

Back

The leading coefficient determines the end behavior of the polynomial function, affecting whether the graph rises or falls as x approaches positive or negative infinity.

Front

What does it mean if a polynomial is positive on an interval?

Back

It means that for every x-value in that interval, the polynomial evaluates to a positive number.