411 REFERENCE · Wikibooks
Algebra/Chapter 10/Polynomial Inequalities
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Definition
A polynomial inequality is an inequality that relates two polynomial expressions to one another as either less than/greater than.
(Note: In this section, LHS denotes the left-hand side and RHS denotes the right-hand side)
Steps
Bring all terms to the LHS so that RHS = 0.
Find the critical values by using either a graph or factorizing.
Draw a number line with the critical values labelled (for > or <, draw an open circle; for ≤ or ≥, draw a close circle).
Use test values to create and complete a sign chart.
Shade the values on the sign chart which satisfy the inequality, and give your answer in interval notation.
Examples
Example 1.
Solve: .
Solution.
Step 1. Bring all the terms to LHS and factorize.
Critical values are −2, −1, 2.