2Monomials 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
3Polynomials Definition: the sum of monomials Special names: Binomial: is the sum of two termsxy + 3xTrinomial: is the sum of three termsa + ab + 6
4Some examples of Monomials Like Terms7xyz, 9xyz, and ½xyz6x, 5x, and 102xUnlike Terms9x and 4 y3ab, 3 bc, and 8 abc
5Adding 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
6Monomials AddedNotice that the coefficients are added but the variable and the exponent remain the same.
7More Monomials AddedBe sure to compare variables and exponents before adding coefficientsThey must be exactly the sameIf they are not LEAVE THEM ALONE
8DegreeOf 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
9NoteThe degree of any non zero constant monomial such as 12 is 0
10The Degree of a Polynomial Is the greatest of the degrees of its terms after it has been simplified.
11Monomials MultipliedTo multiply these monomialsRearrange
12Rule for Multiplying Monomials It’s easy. Just remember toADD theExponents
13Monomial Raised to a Power This means to repeatedly multiply the monomialSoMeans
14Rule for Raising Monomials to a Power It’s easy. Just remember toMultiply theExponents