Title 22 Inequalities.pdf ✅

2. Polynomial Inequalities - Example: Solve the inequality x(x + 2)(x − 3) 3 (x + 4) 2 ≥ 0 [SOLUTION] Step 1: x(x + 2)(x − 3) 3 (x + 4) 2 = 0 x = −4, −2, 0, 3 Step 2 x < −4 x = −4 −4 < x < −2 x = −2 −2 < x < 0 x = 0 0 < x < 3 x = 3 x > 3 x − − − − − 0 + + + x + 2 − − − 0 + + + + + (x − 3) 3 − − − − − − − 0 + (x + 4) 2 + 0 + + + + + + + x(x + 2) (x − 3) 3 (x + 4) 2 − 0 − 0 + 0 − 0 + Solution Set x = −4, −2 ≤ x ≤ 0, x ≥ 3