MATHPOWER TM 10, WESTERN EDITION Chapter 3 Polynomials 3.1 3.1.1.

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Presentation transcript:

MATHPOWER TM 10, WESTERN EDITION Chapter 3 Polynomials

A polynomial is a collection of algebraic terms used to represent a statement. The degree of a term depends upon the exponents of the variables: A term with more than one variable has a degree equal to the sum of the exponents of the variables. Degree 3 The term with the highest degree, determines the degree of the polynomial. Degree 5 Polynomial Terms A monomial is a one-term expression. A binomial is a two-term expression. A trinomial is a three-term expression. A term with only one variable has a degree equal to the exponent of the variable.

4x 3 y x 2 y x 5 y x 7 Degree Therefore, the degree of this polynomial is 9. An expression can be simplified by collecting like terms and adding their coefficients. 1) 20xy xy - 10y 2 x + 22xy 2) (x 2 + 6x + 22) + (3x x - 16) 3) 7x x x x + 12 = 10xy xy = 4x x x 2 + 6x Addition of Polynomials

Collect like terms and add the additive inverse. Or, distribute the negative sign throughout the polynomial. 1. (12x x + 9) - (7x x - 17) = (12x x + 9) - 1(7x x - 17) = 12x x x x + 17 = 5x x (3x 2 + 4x - 18) - (8x x + 12) + (2x 2 + 5) = 3x 2 + 4x x x x = -3x x x x x 2 + 4x ( ) -4x 2 + 6x Subtraction of Polynomials 4x x x 2 - 4x + 22

For monomial multiplication and division, apply the exponent rules. (6x 3 y 2 )(4x 3 y) = 24x 6 y 3 (-10xy 4 )(3x 2 y 3 )= -30x 3 y 7 16x 4 y 5 -4xy = -4x 3 y Multiplying and Dividing Monomials

Pages 102 and odd 54, 55a, Suggested Questions: