Warm-Up: Copy these notesPolynomial Degree Name using

degreeNumber of terms

Name using number of terms

6 0 constant 1 Monomial

5x+9 11 linear 2 Binomial

2 quadratic 3 Trinomial

3 cubic 1 monomial

4 Fourth degree 3 Trinomial

32x

374 2 xx

xxx 328 34

Examples of Monomials

18 z 24x 35.2 xy3

a

ObjectivesThe student will be able to:

1. find the degree of a polynomial.

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

SOL: A.2.b

Why am I learning this1. You can model real life situations

(sports statistics, money, interest, stocks, chemistry, physics, psychology) with polynomials.

2. Projectile Motion- Angry Birds

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.

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 polynomial2

57

2y

y

Which polynomial is represented by

X2

1

1

X

X

X

1. x2 + x + 1

2. x2 + x + 2

3. x2 + 2x + 2

4. x2 + 3x + 2

5. I’ve got no idea!

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

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 + 12x2y3

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

Standard form of a polynomial

Is when the polynomial is in descending order.

1753 24 xxx