Master solving polynomial and rational inequalities using sign charts, critical points, and interval testing techniques.
Solve the polynomial inequality!
Inequality:
Build a sign chart for the polynomial!
Polynomial Factors:
Critical Points:
Inequalities involve polynomial or rational expressions with inequality signs (>, <, ≥, ≤). Unlike equations, we find ranges of values that satisfy the inequality.
Solve: x² - 4 > 0
Step 1: Factor: (x - 2)(x + 2) > 0
Step 2: Critical points: x = -2, 2
Step 3: Test intervals: x < -2 (positive), -2 < x < 2 (negative), x > 2 (positive)
Solution: x < -2 or x > 2
Solve: (x - 1)/(x + 2) > 0
Step 1: Critical points: x = 1 (numerator), x = -2 (denominator)
Step 2: Test intervals: x < -2 (positive), -2 < x < 1 (negative), x > 1 (positive)
Solution: x < -2 or x > 1