2 Monomials definedA number like 6, 10, or 958(called a constant or a constant monomial)A variable like x, y, or zA product ( that means multiply) of a number and one or more variables
3 Polynomials Definition: the sum of monomials Special names: Binomial: is the sum of two termsxy + 3xTrinomial: is the sum of three termsa + ab + 6
4 Some examples of Monomials Like Terms7xyz, 9xyz, and ½xyz6x, 5x, and 102xUnlike Terms9x and 4 y3ab, 3 bc, and 8 abc
5 Adding Monomials is Magic!!! When monomials have exactly the same variables including the same exponents they are called LIKE TERMSLIKE TERMS can be added by adding their coefficients
6 Monomials AddedNotice that the coefficients are added but the variable and the exponent remain the same.
7 More Monomials AddedBe sure to compare variables and exponents before adding coefficientsThey must be exactly the sameIf they are not LEAVE THEM ALONE
8 DegreeOf a variableThis just means the number of times the variable occurs as a factor in the monomialThe x is of degree 2Of a monomialThis means the sum of the degrees of the variablesThe degree ofis = 7
9 NoteThe degree of any non zero constant monomial such as 12 is 0
10 The Degree of a Polynomial Is the greatest of the degrees of its terms after it has been simplified.
11 Monomials MultipliedTo multiply these monomialsRearrange
12 Rule for Multiplying Monomials It’s easy. Just remember toADD theExponents
13 Monomial Raised to a Power This means to repeatedly multiply the monomialSoMeans
14 Rule for Raising Monomials to a Power It’s easy. Just remember toMultiply theExponents