Objectives�The student 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

What about poly?

one or more

A polynomial is a monomial or a sum/difference of monomials.

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Important Note!!

An expression is not a polynomial if there is a variable in the denominator.

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

1) 7y - 3x + 4

trinomial

2) 10x³yz²

monomial

3)

not a polynomial

The degree of a monomial is the sum of the exponents of the variables.�Find the degree of each monomial.

1) 5x²

2

2. 4a⁴b³c

8

3. -3

0

To find the degree of a polynomial, find the largest degree of the terms.

1) 8x² - 2x + 7

Degrees: 2 1 0

Which is biggest? 2 is the degree!

2) y⁷ + 6y⁴ + 3x⁴m⁴

Degrees: 7 4 8

8 is the degree!

Find the degree of x⁵ – x³y² + 4

1. 0
2. 2
3. 3
4. 5
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.

Put in descending order:

1. 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

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

-2x + 3y - 6x³y² + 12x²y^3�

4. Put in ascending order:

5a³ - 3 + 2a - a²

-3 + 2a - a² + 5a³

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

1. x⁴ + 4xy – x³y²– 2x²y³
2. – 2x²y³ – x³y² + 4xy + x⁴
3. x⁴ – x³y²– 2x²y³ + 4xy
4. 4xy – 2x²y³ – x³y² + x⁴