Beyond the EU: DORA and NIS 2 Directive's Global Impact
3 2 polynomial inequalities
1. 3-2 Polynomial
Inequalities
in One Variable
Objective:
Solve polynomial inequalities in one variable by:
1. Using a sign graph
2. Analyzing a graph of P(x)
2. Polynomial Inequalities
• If P(x) is a polynomial, then P(x) > 0 and
P(x) < 0 are polynomial inequalities.
•We will learn two methods to solve:
1. Using a sign graph
2. Analyzing a graph of P(x)
3. Method 1 – Using a Sign Graph
• Use if the polynomial is factorable.
• Factor to find zeros
• Plot on a number line
• Test values from each interval to
determine the sign of P(x)
• Hint:
• P(x) < 0 means find negative intervals
• P(x) > 0 means find positive intervals
4. Example 1
• Solve x3 – 2x2 – 3x < 0 using a sign graph.
8. Rational Inequalities
• Use same method for rational inequalities
where P(x) and Q(x) are polynomials.
To solve:
• Plot all zeros of numerator and denominator
• Use an open dot for zeros of the
denominator
▫ they make the function undefined: not part of
solution
• Check all intervals, don’t assume signs
alternate!
11. Method 2 – Analyze the Graph
• Useful for functions that are not
factorable.
• Graph the function on the calculator.
• Find zeros using trace
• P(x) > 0 where graph is above x-axis
• P(x) < 0 where graph is below x-axis
12. Example 4
• Solve 2x3 + x2 – 8x + 3 > 0 using a
graphing calculator.