Chapter 88-1,8-2,8-7

By Trevor, Sean and Jamin

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 monomialsStandard Form of a Polynomial - the degree of monomial termsDegree of Polynomial - in one variable is the same as the degree of the monomial(ex.4x) with the greatest exponent.Binomial - Two variables per problemTrinomial- Three variables per problemExamples -Polynomials:Monomial: 4x=Binomial: 4x+2x=Trinomial: 4x+2x+5x=

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 + 77x^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

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^2Add exponents = -20y^6 + 12y^4 - 8y^2

Another example, Finding the Common FactorFind the common factor of the terms  

Sean 8-2

 

Multiplying and Factoring Sean smells goodUse 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.  

Jamin 8-7Factoring Special CasesVocabulary - 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

8-7, Continued

E.g. 2The 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

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

8-7, Continued Questions

Factor1. x^2+6x+9                                                    2. 9x^2-13. xy-5y-2x+104. x^2+5x+65. 2(x+3)=2(x)+2(3)=2x+6  

                                            Answers

1. , 2. , 3. , 4. , 5.