CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 2. Polynomials and Rational Functions

2.3 Polynomial Expansion and Pascal’s Trian-

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Here you will explore patterns with binomial and polynomial expansion and find out how to get coefficients using
Pascal’s Triangle.
The expression( 2 x+ 3 )^5 would take a while to multiply out. Is there a pattern you can use?

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/60704

http://www.youtube.com/watch?v=NLQmQGA4a3M James Sousa: The Binomial Theorem Using Pascal’s Triangle

Guidance

Pascal was a French mathematician in the 17thcentury, but the triangle now named Pascal’s Triangle was studied
long before Pascal used it. The pattern was used around the 10thcentury in Persia, India and China as well as many
other places.

The primary purpose for using this triangle is to introduce how to expand binomials.