Topic 8 Polynomial Operations Book Lessons 17 1

Topic 8 Polynomial Operations Book Lessons 17. 1, 17. 2, 17. 3, 18. 1, 18. 2, 18. 3 Pages 805 - 876 Homework (Due Friday 02/22) Algebra Nation – Section 1 – Topic 2 and 3 Topic 8 and 9 Assessment – March 21 and 22

Overview Topic 8 – Polynomial Operations A) What is a polynomial? B) Adding and Subtracting Polynomials C) Multiplying Polynomials D) Factoring

What is a Polynomial? • Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term"). . . so it says "many terms“ • In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs. • In a polynomial, all variables must be in the numerator and they cannot contain negative exponents. Exponents cannot be variables.

Parts of a Polynomial Variable Coefficient Exponent (power) 2 3 x – 2 xy + 6 Terms Constant

Classifying each term in a polynomial • • Cubic term – Exponent is 3 Quadratic term – Exponent is 2 Linear term – Exponent is 1 Constant term – Exponent is 0 (no variable) 3 x 3 – 4 x 2 + 9 x - 5

Degree of a Polynomial • The largest exponent or the largest sum of exponents of a term within a polynomial

Leading Coefficient • The coefficient of the first term of a polynomial written in descending order of exponents

Like terms are terms whose variables and their exponents are the same. In other words, terms that are "like" each other. (Note: the coefficients can be different) Circle like terms the same color 3 x 2 y 5 y 3 -4 x 2 10 x 2 y 10 2 x 2 -12 y 6 y -8 -y 3

Adding Polynomials Closure property: closed under addition of polynomials (2 g 2 + 6 g – 4) + (g 2 – g)

Subtracting Polynomials Closure property: closed under subtraction of polynomials (4 x 2 + 5) – (– 2 x 2 + 4 x – 7)

Classwork - Complete and turn in work at the end of class