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Chapter 7 Review You Should Remember…. • A polynomial is an algebraic expression consisting of one or more terms separated by addition (+) or subtraction (-) signs. • 3x 3x+2 3x+2y+2 Is a monomial Is a binomial (it has ONE term) (it has TWO terms) Is a trinomial (it has THREE terms) Combining Like Terms • Polynomials that are the SAME can be combined. In order for a polynomial to be considered the SAME they must have the same LITERAL coefficient. • The non-numeric (letter) of a term is it’s literal coefficient. • For example: 2x and 3x are like terms because they both have an x as their literal coefficient. Therefore they can be combined. • Ex. 2x + 3x = 5x Like terms…. • You can also think of terms as tiles; if they are the same tile, they are like terms and they can be combined. • Ex: x + x = 2x Common Factors • Factors are the numbers that are multiplied to produce a specific product. • For example the factors of 12 are: 1 and 12; 2 and 6; 3 and 4 • Common factors are the factors that 2 or more terms have in common. • For example: 12 and 6 both have 1, 2, 3, 6 as factors. Their GCF (greatest common factor is 6. Common Factors of Polynomials • There are 2 ways to find the common factors of a polynomial: – the sharing model (which works well when the common factor is a numerical) – the area model (which works well when the common factor is literal) Sharing Model • The sharing model is used to put a polynomial in a number of groups with each group having the same tiles. • For example: 3x + 12 can be made into 3 groups with x + 4 in each group. Area Model • In the area model, the tiles are arranged to form a rectangle and then the dimension of the rectangle are found: width = 3 length = x + 4 3 X+4 Area Model… • This rectangle has an area of x2 + 2x and it’s dimensions are x and x + 2 X x2 x X+2 x Chapter 7 Review • Page. 362-363 # 1, 2, 3, 5, 6, 13, 14, 15