2/17/14

Silent Solvingwith a Partner

1) Solve by factoring: x3 – 2x2 + 4x – 8

Silent Solvingwith a Partner

2) Solve by factoring: x4 – 12x2 + 11

Silent Solvingwith a Partner

3) Write a polynomial with these roots:

1, 2, 3/5

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?

Silent Solvingwith a Partner

5) Solve by factoring: x4 + 3x3 – 21x2 – 48x + 80

Silent Solvingwith a Partner

6) Write a polynomial with these roots:

-5, 3i, √2

2/18/14

2/19/14

HW Qs? H8: WS

History and Creation of Pascal’s Triangle

The Chinese developed the same triangle in 1261.

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 = 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?

5-72/19 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? H9: p. 329-330 #9-15 odd, 27, 29, 55,

59-67 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

(n + 1) Point Principle