Polynomial and Rational Inequalities with Sign Charts Worksheet with Answer Key

What's on the worksheet

1. Let $f
   f(x) > 0f(x) \ge 0f(x) < 0f(x) \le 0
2. Move every term to one side and factor completely, then solve with a sign chart.
   2x^3 + 6x^2 < 8xx^3 + 2x^2 - 4x - 8 \ge 0x^3 - 7x + 6 < 0
3. Solve each inequality.
   \dfrac{x^2}{x - 2} \le x + 1\dfrac{1}{x} + \dfrac{1}{x - 2} \ge 0\dfrac{x^2 - 4}{x^2 - x - 2} \ge 0
4. Solve (x + 6)²(x - 2)(x - 7) ≤ 0.
5. Samir solves x³ > 9x like this:
6. A mixing tank at a paint store holds 16 liters of paint, and 4 liters of it are blue tint.