1. Monomial a number, variable, or product of either with only exponents of 0 or positive integers.

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• 1.) Monomial - a number, variable, or product of
  either with only exponents of 0 or positive
  integers.
• y, -x, ab, 1/3x, x2, 8, xy2, (abc2)3

Examples
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Special Note

• 1.) Monomial - No monomial has a variable as an
  exponent, nor does it have a variable in the
  denominator of a fraction.
• 3/y, xa

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Terms to write down

• 2.) Polynomial - is the sum or difference of
  monomials.
• Any Monomial is also a polynomial
• a-b, 7-x, -2x2 xy-3,
• 1/8x - xy2, r 9, 6

Examples
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Adding Polynomials

• Add 5x 7 and 8 - 2x

(5x 7)
(-2x 8)


3x 15
or
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Adding Polynomials

• Add 5x 7 and 8 - 2x

line up the
5x 7
-2x 8
like terms

3x 15
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Subtracting Polynomials

• subtract 3a b from 7a 5b

(3a b)
(7a 5b)

-
7a 5b -3a - b

7a -3a 5b - b
4a 4b
or
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Subtracting Polynomials

• Subtract 3a b from 7a 5b

line up the
(7a 5b)
(3a b)
like terms
-
4a 4b
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Adding Polynomials

• Add c2 5c 4 and 3c - 7

c2 5c 4
3c - 7


c2 5c 3c 4 - 7
c2 8c - 3
or
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Adding Polynomials

• Add c2 5c 4 and 3c - 7

line up the
c2 5c 4
3c - 7
like terms

c2 8c - 3
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Monomials

• Have one term such as
• 6, 7a, 5x2, -4m3n2

Why is
a monomial?
-4m3n2
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Binomials

• Have two terms such as
• 5x 3, 6y2 - 2,
• a - b, 2x2y - 3xy2

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

• Have three terms such as
• 3x2 5x - 6
• -3m m3 -2

Notice
The terms are separated by two operation signs (
or -)
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Be ready to answer the following questions

• 1.) What separates the terms of a polynomial?
• 2.) How many signs separate the terms of a
  trinomial?

operation signs
2
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Which of these are monomials?

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

Why aren't the others Monomials?
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Which of these are Polynomials?

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

Why isn't 1/x y a polynomial?
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Clssifying Polynomial

• Polynomials are Classified by degree.
• The Degree is determined by the exponents of the
  terms.

For example
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The degree of a Monomial

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

Monomial Degree
x3 3
x3 y2 5
3x3 y2 5
32x3 y2 5
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The degree of a Monomial

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

Monomial Degree
9 0
x 1
x y 2
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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
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The degree of a Polynomial
Polynomial
Degree
3x2 5x 7 2
3x2 -9xyz yz 3
x y 7 1
2x2 7x -3y-2x2 1
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ascending
going up
the stairs
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descending
going down
the stairs
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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
2
1
0
3
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Ascending order of Polynomials

• From the lowest degree to the highest degree of
  the terms.
• 7 5x 3x2
• 7 - 2x 5x2 3x3

1
0
2
3
2
1
0