Math 12 1.7: Polynomial and Rational Inequalities
Test-Point Method: Used for solving polynomial and rational inequalities
Steps:
1. Move all terms to one side of the inequality (left). If the nonzero side of the equation
involves fractions, combine all terms with a common denominator.
2. Factor the nonzero side of the inequality.
3. Set each of the factors equal to zero and solve for the variable. We call these numbers the
critical numbers. These are the values that are equal to zero.
4. Create a number line labeling the critical numbers. These numbers divide the number line
into intervals.
5. Choose a number within each of the intervals and substitute it in the factored expression to
determine the sign of the result, either positive or negative.
6. Interpret your results. Be sure to check whether the inequality is satisfied by some or all
of the endpoints of the intervals.
Solve each inequality by the test-point method. Write the solution in interval notation.
EX1 - Polynomial:
(
)
(
)
(
)
213xxx+−−<0
EX2 - Rational: 22
11
x
x
+≤
+ We will do this on the other side of the page.