Chapter 10 - Polynomials The word polynomial comes from

the latin base "-Poly-" meaning

"many" and the base "-nomial-"

meaning "terms" The Vertical Motion model expression is an example of a polynomial. -16t + vt + h 2 We have been working with polynomials all year. Polynomials are math expressions that involve terms. Think of a term like a word in a sentence except instead of spaces between terms we use addition symbols

Practice Center Lets get some practice. On a whiteboard, write the following expressions and circle the different terms in each one. x + 2x - 2x - 2 2 3 -b - b - 4b - 3 4 2 4y On your whiteboard, create a polynomial that has three terms So we've dealt with terms, lets start dealing with degrees Simply put, the degree of a polynomial is the same as the largest exponent. x 1 Highest Exponent =1

First Degree Polynomial x 2 Highest Exponent = 2

Identify the degree of the following polynomials

4x - 2x + 4 3 2 y-2y-10y 4 5 3 Create a fourth degree polynomial on your whiteboard Now we can use our math vocabulary to describe different polynomials. If Mrs. Adii came in here, and told us that she was trying to solve a four term 3rd degree polynomial, we have a pretty good idea what it looks like already The beauty about polynomials is that they do not include rational exponents, or negative exponents! And they can be added and subtracted with ease! Work as a group to see if you can add/subtract these polynomials. Be sure to show your work on whiteboards! (4x + 2x + 4x ) + (3x - x + 4) 3 2 2 ( 2y - y - 4 ) - ( y - 4) 2 If the Vertical Motion Model is a polynomial, how many terms does it have? -16t + vt + h Second Degree Polynomial 4x + 2x + 2 Highest Exponent = 3

Third Degree Polynomial 3 The only other part of our polynomial expressions that needs to be discussed are the coefficients

Coefficients are the numbers that are being multiplied by our variables in our terms. Polynomials have as many coefficients as they do terms. *Note* Sometimes the coefficients are simply 1, in which case we do not write them. See Example. 4x + x + 24 4 is the coefficient of our first term

1 is the coefficient of our second term

24 is the coefficient of the last term -x + 4x - 2 2 3 -1 is the coefficient of our first term

4 is the coefficient of our second term

-2 is the coefficient of our last term On you whiteboards, classify the following properties of the polynomial below

Number of Terms

Degree of the Polynomial

Coefficients of each term x + 4x -2x + 3x - 2 4 3 2 It is also important that we can graph polynomial functions. All graphs of polynomials have one thing in common. They pass the Vertical Line Test! Chapter 10 Polynomials Prezi

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# Polynomials!

Could Polynomials be any more exciting? I think not!

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