5.4 Polynomial Inequalities
Solving Polynomial Inequalities
1. Write inequality as: f(x) > 0
f(x) < 0
f(x) ≥ 0
f(x) ≤ 0
2. Find and plot the x-intercepts (real zeros).
3. Sketch the graph through the x-intercepts.
You must use your knowledge of End Behavior and X-Axis
Behavior.
4. Observe your graph and solve the inequality (from step 1)
using interval notation.
REMEMBER that:
To Solve give the interval of for which the
graph is
f(x) > 0 x-values above the x-axis
f(x) < 0 x-values below the x-axis
f(x) ≥ 0 x-values above or on the x-axis
f(x) ≤ 0 x-values below or on the x-axis
Practice Problems:
1. (x – 7)2(x + 6) > 0
2. (x + 5)(x + 3)(x - 4) > 0
3. (x - 4)(x - 5)(x - 7) < 0
4. (x - 4)( x2 + x + 1) > 0
5. x3 – 9x2 > 0
6. x3 + 2x2 - 15x > 0
7. x(x + 3)(5 - x) ≥ 0
8. x4 < 36x2
9. x3 ≥ 3x2
