Solving Polynomial Inequalities
Polynomial Inequality –
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In order to solve a polynomial inequality algebraically, you must first determine the roots
of the corresponding equation.
Ex. 1 – State the intervals on which the function −2𝑥(𝑥 + 4)(𝑥 − 4) < 0
Graphically
Ex. 2 - Solve the following cubic (𝑥 + 2)(𝑥 − 3)(𝑥 + 1) ≥ 0
Therefore x1=-2, x2=3 and x3=-1. These 3 roots divide the domain into four intervals.
Number Line
Interval
Value of f(x)
Is f(x) ≥0?
Ex. 3 – Solve the inequality 4𝑥 3 + 12𝑥 2 < 𝑥 + 15
Factor Table
𝑇ℎ𝑒𝑖𝑟 𝑃𝑟𝑜𝑑𝑢𝑐𝑡
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All polynomial inequalities can be solved using graphing technology