How to Solve a Polynomial Inequality Using a Number Line & Sign Analysis

When we are working with a polynomial inequality, we follow a few steps. First, we want to have all of the numbers and variables on one side of the inequality and a zero on the other side. From here, we factor. After this, we set each parenthesis equal to zero and plot those points on a number line. If the inequality is greater than or less than we use an open circle. If the inequality is greater than or equal to OR less than or equal to, we use a closed circle. From here, we pick points and do a sign analysis. This helps us know which sections of our graph are positive and negative. After we figure that out, it is easy to tell which numbers fill in our inequality correctly.

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