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**Polynomials By the end of class, you will be able to:**

1. find the degree of a polynomial. 2. arrange the terms of a polynomial in ascending or descending order.

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**What does each prefix mean?**

mono one bi two tri three

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**What about poly? one or more**

A polynomial is a monomial or a sum/difference of monomials. Important Note!! An expression is not a polynomial if there is a variable in the denominator.

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**State whether each expression is a polynomial. If it is, identify it.**

1) 7y - 3x + 4 trinomial 2) 10x3yz2 monomial 3) not a polynomial

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**Which polynomial is represented by**

X 1 X 1 X2 X x2 + x + 1 x2 + x + 2 x2 + 2x + 2 x2 + 3x + 2 I’ve got no idea!

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**The degree of a monomial is the sum of the exponents of the variables**

The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 1) 5x2 2 4a4b3c 8 -3

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**Which is biggest? 2 is the degree!**

To find the degree of a polynomial, find the largest degree of the terms. 1) 8x2 - 2x + 7 Degrees: Which is biggest? 2 is the degree! 2) y7 + 6y4 + 3x4m4 Degrees: 8 is the degree!

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**Find the degree of x5 – x3y2 + 4**

2 3 5 10

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**A polynomial is normally put in ascending or descending order.**

What is ascending order? Going from small to big exponents. What is descending order? Going from big to small exponents.

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**Put in descending order:**

8x - 3x2 + x4 - 4 x4 - 3x2 + 8x - 4 2) Put in descending order in terms of x: 12x2y3 - 6x3y2 + 3y - 2x -6x3y2 + 12x2y3 - 2x + 3y

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**3) Put in ascending order in terms of y: 12x2y3 - 6x3y2 + 3y - 2x**

-2x + 3y - 6x3y2 + 12x2y3 Put in ascending order: 5a a - a2 -3 + 2a - a2 + 5a3

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**Write in ascending order in terms of y: x4 – x3y2 + 4xy – 2x2y3**

– 2x2y3 – x3y2 + 4xy + x4 x4 – x3y2– 2x2y3 + 4xy 4xy – 2x2y3 – x3y2 + x4

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Do Now: Evaluate each expression for x = -2. Aim: How do we work with polynomials? 1) -x + 12) x 2 - 53) -(x – 6) Simplify each expression. 4) (x + 5)

Do Now: Evaluate each expression for x = -2. Aim: How do we work with polynomials? 1) -x + 12) x 2 - 53) -(x – 6) Simplify each expression. 4) (x + 5)

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