Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

248 views

182 views

182 views

Published on

No Downloads

Total views

248

On SlideShare

0

From Embeds

0

Number of Embeds

4

Shares

0

Downloads

4

Comments

0

Likes

1

No embeds

No notes for slide

- 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.
- 5. You Try! • Solve: 2x2 + 3x – 5 < 0
- 6. Example 2 • Solve (x2 – 1)(x – 4)2 0
- 7. You Try! • Solve: x4 – 4x2 0
- 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!
- 9. Example 3 • Solve
- 10. You Try! • Solve
- 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.
- 13. You Try! • Solve 4x3 – 3x2 – 9x – 2 0

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment