1. Chapter 8 8-1,8-2,8-7 By Trevor, Sean and Jamin

2. Jedom 8-1 Adding and Subtracting Polynomials Vocab - Monomial - is an expression that is a number a variable, or a product of a number and one or more variables(numbahs). Degree of a Monomial - is the sum of the variables. Polynomial - is the sum of one or more monomials Standard Form of a Polynomial - the degree of monomial terms Degree of Polynomial - in one variable is the same as the degree of the monomial(ex.4x) with the greatest exponent. Binomial - Two variables per problem Trinomial- Three variables per problem Examples -Polynomials: Monomial: 4x= Binomial: 4x+2x= Trinomial: 4x+2x+5x=

3. 8-1 Part Duece Degree of a Monomial: Adding Polynomials: Simplify: (4x^2+6x+7)+(2x^2- 9x +1) 2/3x Degree: 1 4x^2 + 6x + 7 7x^2y^3 Degree: 5 +2x^2 - 9x + 1 6x^2 - 3x +8 -4 Degree: 0 Classifying Polynomials: a. 5 - 2x -2x + 5 (place them in order) linear binomial

5. Sean 8-2 continued Examples of Multiplying a Monomial and a Trinomials, Simplify, -4y^2(5y^4 - 3y^2 + 2). -4y^2(5y^4 - 3y^2 + 2) = -4y^2(5y^4) - 4y^2(-3y^2) - 4y^2(2) = -20y^2 + ^4 + 12y^2 + ^2 - 8y^2 Add exponents = -20y^6 + 12y^4 - 8y^2 Another example, Finding the Common Factor Find the common factor of the terms

6. Sean 8-2 Multiplying and Factoring Sean smells good Use Distributive Property to multiply a number by a sum or difference. 5(a + 3) = 5a + 15 (x - 2)(3) = 3x - 6 -2(2y + 7) = -4y - 14 You can also use the Distributive Property or an area model to multiply polynomials. Consider 2x(3x + 1) 2x(3x + 1) = 2x(3x) + 2x(1) = 6x^2 + 2x You can use the Distributive Property for multiplying powers with the same base when multiplying by a monomial.

9. Jamin 8-7 Factoring Special Cases Vocabulary - Perfect Square Trinomial E.g. 1 - Factoring a Perfect-Square Trinomials With A=1 Factor Rewrite first and last terms Does the middle term equal 2ab? 8x=2(x*4) Write the factors as the square of the binomial

10. 8-7, Continued E.g. 2 The area of the square shown at the right is. Find an expression for the length of a side. 9g^2+12g+4=(3g)^2+12g+2g^2 Rewrite 9g^2 as (3g^2) and 4 as 2^2 =(3g)^2+2(3g)(2)+2^2 Does the middle term equal 2ab? 12g=2(3g)(2) =(3g+2)^2 Write the factors as the square of a binomial

12. 8-7, Continued E.g. Factor x^2 -64 x^2-64=x^2-8^2 Rewrite 64 as 8^2 =(x+8)(x-8) Factor

13. 8-7, Continued Questions Factor 1. x^2+6x+9 2. 9x^2-1 3. xy-5y-2x+10 4. x^2+5x+6 5. 2(x+3)=2(x)+2(3)=2x+6 Answers 1.1., 2., 3., 4., 5. 2.3.4.5.