-3x² + 2x + 8 Do Now 2/22/12 Copy HW in your planner.

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-3x² + 2x + 8 Do Now 2/22/12 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, exponents -3x² + 2x + 8

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

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

Objective SWBAT add and subtract polynomials

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

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

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

To Be or Not To Be a Polynomial… 14 – 3x Yes; 1st degree binomial 4x³ Yes; 3rd degree monomial -3 2y No; negative exponent 9 + 3x² + 2yz³ Yes; 4th degree trinomial n 6x + 2x No; variable exponent

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

Subtract Polynomials (4n² + 5) – (-2n² + 2n – 4) Like Terms 4n² + 5 terms that have the same variable (4n² + 5) – (-2n² + 2n – 4) You can subtract polynomials using the vertical or horizontal format. Vertical Format Horizontal Format 4n² + 5 (4n² + 2n²) – 2n + (5 + 4) – (-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? Perimeter is the distance around a figure. Add together each of the sides. 3x – 2 3x - 2 + 2x + 2x + 1 + 5x - 2 (reorder terms) 2x 2x + 1 3x + 2x + 2x + 5x – 2 – 2 + 1 (combine like terms) 12x – 3 5x – 2