Starter – Day 1 November 12 Content Objective: We will use Pascal’s Triangle to expand polynomial expressions faster than calculating them by hand. Let’s create Pascal’s Triangle. Start with 1. 1 Add the numbers above to create the next row. 1 1 Do it again. 1 2 1 Keep repeating that pattern 1 3 3 1 until you get eight (8) rows. 4 6

How are the rows of Pascal’s Triangle generated? LAB Writing How are the rows of Pascal’s Triangle generated? Describe the process you went through to create the eight rows in the starter.

Homework Questions?

Homework: Sign off and turn in 4-1 Polynomial Division (book) 4-2 Complex Zeros – Day 1 Complex Zeros – Day 2 LAB Writings Starters

Pascal’s Triangle and Binomial Theorem These two make expanding polynomials a lot easier! First, some notation: nCk means n choose k. This means “the number of different combinations we can have if, out of n trials, our desired outcome occurs k times.” For example, use nCk if we flip a coin n times and we want to know how many different ways we can have k heads (or k tails, whichever we want). The formula: nCk = Example: find 4C4. Now find 2C3.

More Binomial Theorem When n = 0, we can have 0C0, which equals 1. The values for n = 1 are 1C0 and 1C1, both of which equal 1. For n = 2, 2C0 and 2C2 equal 1, but 2C1 equals 2. Do you see a pattern?

Pascal’s Triangle

Pascal’s Triangle