Polynomial Inequalities

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What is a polynomial inequality?

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A polynomial inequality is an inequality that involves a polynomial expression, typically in the form of f(x) > 0, f(x) < 0, f(x) ≥ 0, or f(x) ≤ 0.

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How do you determine where a polynomial function is greater than zero using a graph?

Back

Identify the intervals on the x-axis where the graph of the polynomial is above the x-axis.

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How do you determine where a polynomial function is less than zero using a graph?

Back

Identify the intervals on the x-axis where the graph of the polynomial is below the x-axis.

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What effect do odd multiplicities have on the x-axis when a polynomial crosses it?

Back

Odd multiplicities cause the polynomial to cross the x-axis at the corresponding root.

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What effect do even multiplicities have on the x-axis when a polynomial touches it?

Back

Even multiplicities cause the polynomial to touch the x-axis and turn around at the corresponding root.

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What is the significance of the roots of a polynomial in solving inequalities?

Back

The roots of a polynomial indicate the points where the polynomial changes sign, which helps in determining the intervals for the inequality.

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What is the first step in solving a polynomial inequality?

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Factor the polynomial expression if possible to find the roots.

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It represents all real numbers less than -4 and between -1 and 2, excluding -1 and 2.