Factoring Trinomials: Jim’s Excellent Adventure

1. Factoring Trinomials: Jim’s Excellent Adventure

2. The Plan Factoring Trinomials – 40 minutes Operations Research- 5 minutes Jim’s Fractured Career- 5 minutes

3. Factor Did you get?

4. Wolfram Alpha says it is OK.

5. Weird, Wonderful but Ugly. So, a road not taken. Find linear factors.

6. Factor into Linear Factors Did you get?

7. This is the “best” linear factorization! Why? Most Useful Easiest to Find

8. Most useful when • Solving equations • Understanding quadratic functions • Simplifying rational expressions • Finding partial fractions

9. Solving equations

10. Understanding quadratic functions

11. simplifying rational expressions

12. Finding partial fractions with traditional factoring

13. Finding partial fractions with ‘new” factoring

14. Easiest to find. First, review factoring trinomials whose leading Coefficient is I. Find two factors of ______ that add to _____. They are ____ and _____. Find two factors of ______ that add to _____. They are ____ and _____. Find two factors of ______ that add to _____. They are ____ and _____. Find two factors of ______ that add to _____. They are ____ and _____.

15. So, fairly easy - may need to be systematic. Now review factoring trinomials whose leading Coefficient is not I.

16. More review factoring trinomials whose leading Coefficient is not I. Find two factors of ______ that add to _____. They are ____ and _____.

17. Now the easy way. Find two factors of ______ that add to _____. They are ____ and _____.

18. Why it works.

19. Why the method works in general. Consider, Find two factors of ______ that add to _______. They are ____ and _____. References: 1. “Factoring the Trinomial ax2+bx+1 When a>1,” Doyne Holder, School Science and Mathematics,Oct. 1,1958,Vol.58,Issue 7,Pages 548-549. 2. “A 16-year-old girl has the math world spinning,” Ronit Feldman, Metrotimes, July 2, 2003. http://www.metrotimes.com/editorial/story.asp?id=5077

20. Where did this idea come from? An old ( first published in 1884) textbook: A College Algebra ,Revised Edition(1902), G.A. Wentworth, pages 452-453.

21. Effectively stretching the X-axis.

22. So, try it you will like it. And help me lead the Revolution!

23. Operations Research Sometimes called Industrial Engineering, Management Science, Quantitative management… Some of the tools used are statistics, optimization, probability, queuing theory, game theory, graph theory, decision analysis, simulation, and computer applications. (Wikipedia) Types of problems solved: project planning, factory layout, efficient reliable telecommunications networks, traffic flow, bus routes, computer chip layout, supply chains, robotics, freight transportation, scheduling, blending … (Wikipedia)

24. Classes Hatton took: Linear Programming, Microeconomics, Linear Algebra, Game Theory, Algorithmic Processes, Network Flows, Macroeconomics, Mathematical Programming, Stochastic Processes, Elementary Statistical Inferences, Reliability Models, Inventory-Production Control, Queuing Theory, Mathematical Systems Theory, Dynamic Programming, Advanced Probability, Large Scale Systems, Decision Theory, Combinatorial Analysis, Applied Probability, Modern Algebra, Advanced Stochastic Processes, and Combinatorial Optimization.

25. Now, Jim’s Fractured Career- • Kirkwood High School St. Louis, Missouri • Rice University Houston, Texas • Stanford University, Palo Alto, California • U.S. Army, St-Louis, Missouri • Stanford University • Massachusetts, Mt Shasta, California • College of the Siskiyous, Weed, California • SOU