2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.
-
Upload
alexandra-barrett -
Category
Documents
-
view
215 -
download
0
Transcript of 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.
![Page 1: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/1.jpg)
2/17/14
![Page 2: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/2.jpg)
![Page 3: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/3.jpg)
![Page 4: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/4.jpg)
Silent Solvingwith a Partner
1) Solve by factoring: x3 – 2x2 + 4x – 8
![Page 5: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/5.jpg)
Silent Solvingwith a Partner
2) Solve by factoring: x4 – 12x2 + 11
![Page 6: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/6.jpg)
Silent Solvingwith a Partner
3) Write a polynomial with these roots:
1, 2, 3/5
![Page 7: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/7.jpg)
Silent Solvingwith a Partner
4) a)List all roots for this polynomial
b) is the function odd or even
c) what is the sign of the leading coefficient?
![Page 8: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/8.jpg)
Silent Solvingwith a Partner
5) Solve by factoring: x4 + 3x3 – 21x2 – 48x + 80
![Page 9: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/9.jpg)
Silent Solvingwith a Partner
6) Write a polynomial with these roots:
-5, 3i, √2
![Page 10: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/10.jpg)
2/18/14
![Page 11: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/11.jpg)
2/19/14
![Page 12: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/12.jpg)
HW Qs? H8: WS
![Page 13: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/13.jpg)
History and Creation of Pascal’s Triangle
The Chinese developed the same triangle in 1261.
Used for solving algebra problems.
![Page 14: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/14.jpg)
BLAISE PASCAL French mathematician
Born in 1623
Child prodigy
At age 19, invented 1st calculating machine (called the Pascaline) to help his father who was a tax collector
Developed the triangle in response to a question on gambling
Died at the age of 39 as a result of poor health
![Page 15: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/15.jpg)
Pascal’s Triangle & Algebra
(x + y)0 = 1
(x + y)1 = 1x + 1y
(x + y)2 = 1x2 + 2xy + 1y2
(x + y)3 = 1x3 + 3x2y + 3xy2 + 1y3
(x + y)4 = 1x4 + 4x3y + 6x2y2 + 4xy3 + 1y4
What is the degree of each term?
![Page 16: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/16.jpg)
5-72/19 Binomial Theorem 50
![Page 17: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/17.jpg)
Binomial Theorem: can use Pascal’s Triangle to expand a BINOMIAL expression.
Example:1) (3x – 5)2
![Page 18: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/18.jpg)
![Page 19: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/19.jpg)
2/20/14
![Page 20: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/20.jpg)
HW Questions? H9: p. 329-330 #9-15 odd, 27, 29, 55,
59-67 odd
![Page 21: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/21.jpg)
![Page 22: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/22.jpg)
2/21/14
![Page 23: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/23.jpg)
![Page 24: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/24.jpg)
Interpolation – between data points (within domain)Extrapolation – prediction beyond data points (beyond domain)
![Page 25: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/25.jpg)
Interpolation – between data points (within domain)Extrapolation – prediction beyond data points (beyond domain)
![Page 26: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/26.jpg)
(n + 1) Point Principle
![Page 27: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/27.jpg)
(n + 1) Point Principle
![Page 28: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/28.jpg)
![Page 29: 2/17/14. Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8.](https://reader035.fdocuments.in/reader035/viewer/2022062500/5697c00a1a28abf838cc7b3b/html5/thumbnails/29.jpg)