Do Now 2/22/10 Copy HW in your planner.Copy HW in your planner. –Text p. 557, #4-28 multiples of 4, #32-35 all In your notebook on a new page define the parts of the expression below. Use the following words: terms, coefficients, constants, exponentsIn your notebook on a new page define the parts of the expression below. Use the following words: terms, coefficients, constants, exponents -3x² + 2x + 8

Chapter 9 “Polynomials and Factoring” (9.1) Add and subtract polynomials(9.1) Add and subtract polynomials (9.2) Multiply polynomials(9.2) Multiply polynomials (9.3) Find special products of polynomials(9.3) Find special products of polynomials (9.4) Solve polynomial equations in factored form(9.4) Solve polynomial equations in factored form (9.5) Factor x² + bx + c(9.5) Factor x² + bx + c (9.6) Factor ax² + bx + c(9.6) Factor ax² + bx + c (9.7) Factor special products(9.7) Factor special products (9.8) Factor polynomials completely(9.8) Factor polynomials completely

Parts of an Expression -3x² + 2x + 8 Terms of the expression Coefficient the number part of the term (negative sign included) Constant Term that has no variable Remember this???

Objective SWBAT add and subtract polynomials

Section 9.1 “Add and Subtract Polynomials” Monomial a number, -3x the sum of the exponents of the variables in the monomial Degree of a Monomial x³yz² or the product of a number and one or more variables with whole number exponents or the product of a number and one or more variables with whole number exponents a variable, a variable, 7 Degree = 1 Degree = 6 Degree = 0

Polynomial a monomial, –3x the greatest degree of its terms Degree of a Polynomial – x³ or the sum (or difference) of monomials or the sum (or difference) of monomials +7 Degree = 1Degree = 3Degree = 0 Leading Coefficient the coefficient of the first term when exponents are decreasing from left to right. Write a polynomial with exponents decreasing from left to right.

Types of Polynomials Binomial 4 – 3x polynomial with 2 terms 2x³+ x – 7 Trinomial polynomial with 3 terms

To Be or Not To Be a Polynomial… 14 – 3x Yes; 1 st degree binomial 4x³ Yes; 3 rd degree monomial 2y No; negative exponent x² + 2yz³ Yes; 4 th degree trinomial 6x + 2x No; variable exponent n

Add Polynomials (2x² + x³ – 1) (2x² + x³ – 1) Like Terms terms that have the same variable (2x³ – 5x² + x) + (2x³ – 5x² + x) + You can add polynomials using the vertical or horizontal format. Vertical Format 2x³ – 5x² + x 2x³ – 5x² + x x³ + 2x² – 1 x³ + 2x² – 1 3x³ – 3x² + x – 1 3x³ – 3x² + x – 1 Horizontal Format (2x³ + x³) + (2x² – 5x²) + x – 1 (2x³ + x³) + (2x² – 5x²) + x – 1 3x³ – 3x² + x – 1 3x³ – 3x² + x – 1

Subtract Polynomials (-2n² + 2n – 4) (-2n² + 2n – 4) Like Terms terms that have the same variable (4n² + 5) – (4n² + 5) – You can subtract polynomials using the vertical or horizontal format. Vertical Format 4n² + 5 4n² + 5 – (-2n² +2n – 4) – (-2n² +2n – 4) Horizontal Format (4n² + 2n²) – 2n + (5 + 4) (4n² + 2n²) – 2n + (5 + 4) 6n² – 2n + 9 6n² – 2n + 9 +(2n² -2n + 4) +(2n² -2n + 4) 6n² – 2n + 9 6n² – 2n + 9

Adding and Subtracting Polynomials

Simplifying Polynomials in Geometry What is the perimeter of the trapezoid? 3x – 2 5x – 2 2x 2x + 1 Perimeter is the distance around a figure. 3x x + 2x x - 2 (reorder terms) (reorder terms) Add together each of the sides. 3x + 2x + 2x + 5x – 2 – (combine like terms) 12x – 3

Homework Text p. 557, #4-28 multiples of 4, #32-35 all