1. Polynomial & Rational Inequalities

2. Polynomial Inequalities
Solve algebraically.
One side of the inequality should be 0.
Find the zeros of the polynomial function.
Divide a number line at these critical values.
Choose a point in each interval and determine the sign of the polynomial in that interval.
Write the solution in interval notation.
(−∞,−2)∪(3,∞)

3. Polynomial Inequalities
Approximate the solution graphically.
Graph the function
Find the zeros (critical points)
(−∞,−2)∪(3,∞)

4. Rational Inequalities
Solve algebraically.
One side of the inequality should be 0.
Find the zeros of the numerator and of the denominator:
Divide a number line at these critical values.
Choose a point in each interval and determine the sign of the polynomial in that interval.
Write the solution in interval notation.
(−2, 2)

5. Rational Inequalities
Approximate the solution graphically.
Graph the function
Find the zeros.
Other Critical Points
(−2, 2)

6. Rational Inequalities
Solve algebraically.
One side of the inequality should be 0 and the other side should be written as a single expression.
In the denominator: 𝑥≠2, 𝑥≠1
Find the critical values in the numerator and the denominator.

7. Rational Inequalities
Divide a number line at these critical values.
Choose a point in each interval and determine the sign of the polynomial in that interval.
Write the solution in interval notation.
(1, 2)

8. Rational Inequalities
Approximate the solution graphically.
Graph the function
Find the zeros.
Other Critical Points
(1, 2)