Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. x^2+2x<0

Key Concepts

Polynomial Inequalities

Polynomial inequalities involve expressions where a polynomial is compared to a value using inequality signs (e.g., <, >, ≤, ≥). To solve these inequalities, one typically finds the roots of the polynomial, determines the intervals on the number line, and tests these intervals to see where the inequality holds true.

Graphing Solution Sets

Graphing solution sets on a real number line visually represents the intervals where the inequality is satisfied. This involves marking the critical points (roots) and shading the appropriate regions based on whether the inequality is strict or inclusive, helping to clearly communicate the solution.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). For example, (a, b) means all numbers between a and b, not including a and b, while [a, b] includes both endpoints.