wk3 dy1 agenda

Wk3Dy1 Binomial Expansion Intro (morrison).notebook

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Wk3 Dy1 Agenda1) EEDN#15 (12min)2) Radical Nspire (8min)3) Adding Polynomials (20min)4) Distribution with Polynomials (30min) 4) FOIL (30min)

OTL: 1) Start POW#122) Add/Sub Polynomial 3) Multiply Polynomials


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What is a polynomial?

Ideas:

Let's start by breaking apart the wordPoly Nomial

Here is where it gets tricky. Everyone knows Poly means many but what does Nomial mean? Well we are unclear because it is a hybrid word of Greek and Latin origin. What this means is it could mean "name" from the Latin word "nomen" or it could mean "law" from the Greek word "nomos". Either way its easier just to see an example.

3x2 + 5x + 3

Term Term Term

Since these terms are not like this is a Polynomial

The best answer to your question may be that nomial may derive from

Greek nomos, "law", influenced by Latin nomen, "name", or perhaps

the other way around, but we don't know for sure.

Doctor Rick, The Math Forum


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So...

Monomial All Like Terms

Binomial two unlike terms

Trinomials three unlike terms

3x + 5x = 8x

Term TermLike

Term

Term

3x + 5

Not LikeTerm Term

Term

3x2 + 5x + 2

Term Term

Not Like

Polynomials Many unlike terms


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Based on what you have learned, create:

1) 5th degree Trinomial

2) 4th degree polynomial with 5 terms

3) 9th degree Binomial


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Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra and algebraic geometry.

Wikipedia's Description of Polynomial

Why Study Polynomials?


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Adding Polynomials

What is the definition of Polynomials that makes the most sense for what we are doing?

So if we are adding terms, the same rules apply that we can only add LIKE terms.Back to the Nspires.


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MULTIPLYING POLYNOMIALS!!What we were all waiting for!!

So you have the basics of multiplying variables...

x*x = x2

3x * x = 3x2

7x5 * 3x2 = ?So my question is that does Distribution work like it should on variables?

x (3 + x) = 3x + x2

x( x + 3x2) = x2 + 3x3Do You Agree?

Back to Nspires


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F.O.I.LIs there a pattern or strategy we have for multiplying binomial pairs?

First Outside Inside

Last

(2n+2)(6n+1)First

Outside

(2n+2)(6n+1)Inside

Last

First = 12n2Outside = 2nInside = 12nLast = 2

There are 4 terms but the outside and inside are LIKE and we ALWAYS combine LIKE TERMS

SO...

12n2 + 14n +2

Let's Practice


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