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

2. 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: 3.1.2 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.

3. 4x 3 y 4 + 16x 2 y 3 - 10x 5 y 4 - 20x 7 Degree 7 5 9 7 Therefore, the degree of this polynomial is 9. An expression can be simplified by collecting like terms and adding their coefficients. 1) 20xy 2 + 16xy - 10y 2 x + 22xy 2) (x 2 + 6x + 22) + (3x 2 + 10x - 16) 3) 7x 2 + 16x - 14 3x 2 - 10x + 12 = 10xy 2 + 38xy = 4x 2 + 16x + 6 10x 2 + 6x - 2 3.1.3 Addition of Polynomials

4. Collect like terms and add the additive inverse. Or, distribute the negative sign throughout the polynomial. 1. (12x 2 - 16x + 9) - (7x 2 + 22x - 17) = (12x 2 - 16x + 9) - 1(7x 2 + 22x - 17) = 12x 2 - 16x + 9 - 7x 2 - 22x + 17 = 5x 2 - 38x + 26 2. (3x 2 + 4x - 18) - (8x 2 + 15x + 12) + (2x 2 + 5) = 3x 2 + 4x - 18 - 8x 2 - 15x - 12 + 2x 2 + 5 = -3x 2 - 11x - 25 3. 4x 2 + 10x - 16 8x 2 + 4x - 22 -1( ) -4x 2 + 6x + 6 3.1.4 Subtraction of Polynomials 4x 2 + 10x - 16 -8x 2 - 4x + 22

5. 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 4 3.1.5 Multiplying and Dividing Monomials

6. Pages 102 and 103 1 - 51 odd 54, 55a, 59 3.1.6 Suggested Questions: