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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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 (5x + 7) (-2x + 8) + = or

Adding Polynomials Add 5x + 7 and 8 - 2x line up the 5x + 7 -2x + 8 like terms + 3x + 15

Subtracting Polynomials subtract 3a + b from 7a + 5b (7a + 5b) (3a + b) = - 7a + 5b -3a - b = 7a -3a + 5b - b 4a + 4b or

Subtracting Polynomials Subtract 3a + b from 7a + 5b line up the (7a + 5b) (3a + b) like terms - 4a + 4b

c2 + 8c - 3 c2 + 5c + 4 3c - 7 c2 + 5c + 3c + 4 - 7 Adding Polynomials Add c2 + 5c + 4 and 3c - 7 c2 + 5c + 4 3c - 7 + = c2 + 5c + 3c + 4 - 7 c2 + 8c - 3 or

c2 + 8c - 3 c2 + 5c + 4 3c - 7 Adding Polynomials Add c2 + 5c + 4 and 3c - 7 line up the c2 + 5c + 4 3c - 7 like terms + c2 + 8c - 3

Monomials Have one term such as: 6, 7a, 5x2, -4m3n2 -4m3n2 Why is a monomial? -4m3n2

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 -)

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

Which of these are monomials? 1.) x2 y2, x2 /y2, 1/7, ax2 + bx + c, 1/x + y Why aren't the others Monomials?

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?

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. Monomial Degree x3 3 x3 y2 5 3x3 y2 5 32x3 y2 5

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

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 2 1 3

Ascending order of Polynomials From the lowest degree to the highest degree of the terms. 7 + 5x + 3x2 7 - 2x + 5x2 + 3x3 1 2 3 1 2