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Journal Entry #10: Polynomial Review

Journal Entry #10: Polynomial Review. December 2013. Using alge-tiles:. Each tile has the dimensions that result in the following areas: When the tiles are turned over to show the white sides, it represents the negative value. y 2. y. x. 1. xy. x 2. -y 2. -1. -xy. -x 2.

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Journal Entry #10: Polynomial Review

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  1. Journal Entry #10: Polynomial Review December 2013

  2. Using alge-tiles: Each tile has the dimensions that result in the following areas: When the tiles are turned over to show the white sides, it represents the negative value. y2 y x 1 xy x2 -y2 -1 -xy -x2 -y -x

  3. Zero Principle Zero can be represented by two like quantities with opposite signs. x2 -x2

  4. Polynomial Terms: • Term: an expression formed by the product of numbers and variables. • Numerical Coefficient: the numeric part of the term (the number). • Variable: the non-numeric part of the term (the letter) ~ Sometimes this is called the literal coefficient. • Polynomial: an algebraic expression consisting of one or more terms that are being added or subtracted. A monomial has ONE term (ex. 3x2) A binomial has TWO terms (ex. 3x2 – 2x) A trinomial has THREE terms ((ex. 3x2 – 2x - 1)

  5. Factors • When two or more integers are multiplied, each integer is a factor of the product. The factors of 12 are 1, 2, 3, 4, 6, 12. • The largest factor that two or more numbers have in common is called the greatest common factor (GCF). The factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 18 are 1, 2, 3, 6, 9, 18. The GCF is 6.

  6. More Polynomial Terms • An algebraic model is a model that represents a relationship by an equation or formula, or represents a pattern of numbers created by an algebraic expression. • Like terms are terms that have the same variable (or literal coefficient). • The commutative property states that numbers can be added or multiplied in any order. a + b = b + a or a x b = b x a

  7. Distributive Property A rule for expanding an expression within brackets by multiplying each term inside the bracket by the term outside the brackets. For example: 4(x + 2) = (x + 2) + (x + 2) + (x + 2) + (x + 2) = 4(x) + 4(2) = 4x + 8 This property allows you to simplify expressions involving the multiplication of a monomial by a polynomial: a(x + y) = ax + ay

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