Bellwork

2.) : .

Any Monomial is also a polynomial

a-b, 7-x, -2x2 +xy-3,

1/8x - xy2, r + 9, 6

5x + 7 8 2x

(5x + 7)

(-2x + 8)

3x + 15

+

=

5x + 7 8 2x

5x + 7

-2x + 8

3x + 15

+

3a + b 7a + 5b

(3a + b)

(7a + 5b)

4a + 4b

-

=

7a + 5b -3a - b

=

7a -3a + 5b - b

3a + b 7a + 5b

(3a + b)

(7a + 5b)

4a + 4b

-

Add c2 + 5c + 4 and 3c - 7

+

=

c2 + 5c + 4

3c - 7

c2 + 8c - 3

c2 + 5c + 3c + 4 - 7

c2 + 5c + 4 3c 7

+

c2 + 5c + 4

3c - 7

c2 + 8c - 3

Monomials

Have one term such as:

6, 7a, 5x2, -4m3n2

Why is

-4m3n2

a monomial?

Binomials

Have two terms such as

5x + 3, 6y2 - 2,

a - b, 2x2y - 3xy2

Notice:

The terms are separated by one operation sign (+ or -)

Trinomials

Have three terms such as:

3x2 + 5x - 6

-3m + m3 -2

Notice:

The terms are separated by two operation signs (+ or -)

Which of these are monomials?

1.) x2 y2, x2 /y2, 1/7, ax2 + bx + c, 1/x + y

Why aren't the othersMonomials?

Which of these are Polynomials?

1.) x2 + y2, x3, x2 - 1/3, ax2 + bx + c, 1/x + y

Why isn't 1/x + ya polynomial?

Clssifying Polynomial

Polynomials are Classified by degree.

The Degree is determined by the exponents of the terms.

For example:

The degree of a Monomial

Is the sum of the exponents of the variables of the monomial.

x3 3

x3 y2 5

MonomialDegree

3x3 y2 5

32x3 y2 5

The degree of a Monomial

Is the sum of the exponents of the variables of the monomial.

MonomialDegree

x 1

x y 2

9 0

The degree of a Polynomial

Is the highest degree of any of its terms after the poly has been simplified.

Polynomial Degree

3x2 + 5x + 7 2

The degree of a Polynomial

Polynomial Degree

3x2+ 5x + 7 2

3x2 -9xyz +y+z 3

x + y + 7 1

2x2 +7x -3y-2x2 1

ascending

going up

the stairs

descending

going down

the stairs

Descending order of Polynomials

From the highest degree to the lowest degree of the terms.

3x2 + 5x + 7

3x3 + 5x2 - 2x + 7

2

1

0

3

2

1

0

Ascending order of Polynomials

From the lowest degree to the highest degree of the terms.

7 + 5x + 3x2

7 - 2x + 5x2 + 3x3

2

1

0

3

2

1

0