•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

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

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

Adding Polynomials•Add 5x + 7 and 8 - 2x

Adding Polynomials•Add 5x + 7 and 8 - 2x

Subtracting Polynomials•subtract 3a + b from 7a + 5b

Subtracting Polynomials•Subtract 3a + b from 7a + 5b

Adding Polynomials•Add c2 + 5c + 4 and 3c - 7

c2 + 5c + 4 3c - 7

c2 + 8c - 3

c2 + 5c + 3c + 4 - 7

Adding Polynomials•Add c2 + 5c + 4 and 3c - 7

c2 + 5c + 43c - 7

c2 + 8c - 3

Monomials•Have one term such as:

•6, 7a, 5x2, -4m3n2

-4m3n2

Binomials•Have two terms such as

•5x + 3, 6y2 - 2,

•a - b, 2x2y - 3xy2 The terms are separated by one operation sign (+ or -)

Trinomials•Have three terms such as:

• 3x2 + 5x - 6• -3m + m3 -2

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

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?

Which of these are monomials?

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

Which of these are Polynomials?

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

Clssifying Polynomial

•Polynomials are Classified by degree.

•The Degree is determined by the exponents of the terms.

The degree of a Monomial•Is the sum of the exponents of the variables of the monomial.

x3 3x3 y2 5

Monomial Degree

3x3 y2 532x3 y2 5

The degree of a Monomial•Is the sum of the exponents of the variables of the monomial.

Monomial Degree

x 1x 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 23x2 -9xyz +y+z 3x + y + 7 12x2 +7x -3y-2x2 1

Descending order of Polynomials• From the highest degree to the

lowest degree of the terms.

•3x2 + 5x + 7

•3x3 + 5x2 - 2x + 7

Ascending order of Polynomials• From the lowest degree to the

highest degree of the terms.

•7 + 5x + 3x2

•7 - 2x + 5x2 + 3x3