2/17/14

Silent Solving with a Partner 1) Solve by factoring: x 3 – 2x 2 + 4x – 8

Silent Solving with a Partner 2) Solve by factoring: x 4 – 12x

Silent Solving with a Partner 3) Write a polynomial with these roots: 1, 2, 3/5

Silent Solving with 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?

Silent Solving with a Partner 5) Solve by factoring: x 4 + 3x 3 – 21x 2 – 48x + 80

Silent Solving with a Partner 6) Write a polynomial with these roots: -5, 3i, √2

2/18/14

2/19/14

HW Qs? HW Qs? H8: WS

History and Creation of Pascal’s Triangle The Chinese developed the same triangle in Used for solving algebra problems.

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

Pascal’s Triangle & Algebra (x + y) 0 = 1 (x + y) 1 = 1x + 1y (x + y) 2 = 1x 2 + 2xy + 1y 2 (x + y) 3 = 1x 3 + 3x 2 y + 3xy 2 + 1y 3 (x + y) 4 = 1x 4 + 4x 3 y + 6x 2 y 2 + 4xy 3 + 1y 4 What is the degree of each term?

5-7 2/19 Binomial Theorem 50

Binomial Theorem: can use Pascal’s Triangle to expand a BINOMIAL expression. Example: 1) (3x – 5) 2

2/20/14

HW Questions? HW Questions? H9: p #9- 15 odd, 27, 29, 55, odd

2/21/14

Interpolation – between data points (within domain) Extrapolation – prediction beyond data points (beyond domain)

Interpolation – between data points (within domain) Extrapolation – prediction beyond data points (beyond domain)

(n + 1) Point Principle