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≤4x−2

Polynomial inequalities involve expressions where a polynomial is compared to a value using inequality symbols (e.g., ≤, ≥, <, >). To solve these inequalities, one typically finds the roots of the corresponding polynomial equation and tests intervals between these roots to determine where the inequality holds true.

Interval notation is a mathematical notation used to represent a range of values on the real number line. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). For example, the interval [a, b) includes 'a' but not 'b'.

Graphing solutions on a number line visually represents the solution set of an inequality. Each solution is marked with a solid dot for included endpoints and an open dot for excluded endpoints, while shading indicates the range of values that satisfy the inequality. This helps in understanding the solution's extent and boundaries.