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    7.6 notes b 7.6 notes b Document Transcript

    • Opener: 1.) Find all solutions to the following equation:                                 10x3 + 8x2 = 0 Complete each of  the following  problems in your  notes. 2.) Factor out the GCF of the following expression:                                 10x4y ‐ 18x2 3.) Write each expression as a product of expressions:                                 3b2 ‐ 15b + b ‐ 5 1
    • Homework  Questions: 2
    • 7.6   Anatomy of a Polynomial Topic One: Examine the examples of polynomials below.  What do  Defining a Polynomial you think a polynomial is?  Write down how you think  you might define one. x2‐1 3x+5y+1 2x3‐9x4‐3x+2 y2‐x3‐xy   x x3‐8x2+1             3 Polynomial: an expression that you write as the sum of  one or more monomials. Monomial: Product of a number, coefficient, and one  more variable raised to nonnegative integer powers. 3
    • Topic Two: Degree of a  Degree of a Monomial:  Monomial • One Variable: exponent of the variable (Ex. 1 & 2) 5x2   5 • >One Variable: sum of the exponents of each variable (Ex. 3 & 4) 5x2y3 x2(x3y5) It's Your Turn!!! Name the coefficient, variable, and degree of each  monomial. 3x2 ‐4a5 b3 ‐.5 7x3y5 4
    • Topic Three:  Classifying  Degree of a Polynomial: Largest degree among all the  Polynomials monomials in the polynomial. (Ex. 5 & 6) Naming a Polynomial: Degree  Type of Polynomial  1  linear  2  quadratic  3  cubic  4  quartic  5  quintic  5
    • Topic Four: Basic Arithmetic with  Polynomials Expand each expression.  Combine like terms to get a  polynomial answer. *Like terms: same variables  & same exponents 2 3 2 (Ex. 7 ) 3x ‐7x+1‐2(10x ‐x +3x) 2 (Ex. 8 ) (3x‐1)(x +2x+5) 6
    • Topic Four: Basic Arithmetic with  Use the following polynomials to help you complete  Polynomials the statements below. x2+4x+5 ‐2x5+7x‐1 3x+7 14x 9 The degree of a product of two nonzero polynomials  is.... The degree of the sum of two nonzero polynomials is... 7
    • Homework:  • Polynomial Worksheet • Mini Writing # 1 8
    • 9