Unit 2: Polynomial Equations and Inequalities Lesson 8: Solving Polynomial Inequalities Properties of inequalities Let a, b and c be real numbers. Transitive Property If a < b and b < c then a < c Addition Property If a < b then a + c < b + c Subtraction Property If a < b then a - c < b - c Multiplication Property If a < b and c is positive then ca < cb If a < b and c is negative ca > cb Note: If each inequality sign is reversed in the above properties, we obtain similar properties. If the inequality sign < is replaced by <= ( less than or equal) or the sign > is replaced by >= ( greater than or equal ), we also obtain similar properties.

Example 1: Solve the inequality 2x - 6 > 4x + 2

Example 2: Given the graph of y = f(x) below, when is f(x) > 0? a)

b)

Example: 3: Example a) Solve x2 > 36 algebraically.

a) Determine an equation for the family of polynomial functions with roots 2, -5 and 3.

b) Solve x2 > 36 graphically.

Example 4: Solve 0 < x3 - 7x + 6 by graphing.

1) Determine the zeros.

2) Factor.

3) Graph and determine where the graph is above the x axis (in this instance . . . . below if the inequality had been different.) Classwork and Homework:

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