Here are the essential concepts you must grasp in order to answer the question correctly.
Polynomial Inequalities
Polynomial inequalities involve expressions where a polynomial is compared to zero using inequality signs (e.g., ≥, ≤, >, <). To solve these inequalities, one must determine the intervals where the polynomial is either positive or negative. This often requires finding the roots of the polynomial and testing intervals between these roots.
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Interval Notation
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 intervals) or excluded (open intervals). For example, the interval [a, b) includes 'a' but not 'b', while (a, b) excludes both endpoints.
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Graphing Solution Sets
Graphing solution sets on a real number line visually represents the intervals where the polynomial inequality holds true. This involves marking the critical points (roots) and shading the regions that satisfy the inequality. Understanding how to accurately depict these intervals helps in interpreting the solution effectively.
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Graphing Polynomial Functions