wk3 dy1 agenda
TRANSCRIPT
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
Wk3Dy1 Binomial Expansion Intro (morrison).notebook
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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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