Chapter 8

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L42 Multiplying and Factoring: Chapter 8 lesson 2

L43 Multiplying Binomials: Chapter 8 lesson 3

Polynomials are classified into monomials, binomials, trinomials, and polynomials. Monomials are only one term for example, 6X^2

L41 Adding and Subtracting Polynomials: This was the first lesson of chapter 8.

Binomials are 2 terms for example, 7x + 3xy^2. Trinomials are three terms for example, 9 + 3x^2 + 12y^7. Polynomials are equations with more than 4 terms, but when referring to all types of nomials, they are called polynomials

Also, other ways of recognizing what type of polynomial it is by using degree. A number such as 5 is constant, 9x + 7 is linear.

9y^2 + 3 is a quadratic, 2xy^3 is cubic, and anything over 3 is called the number for example 4y^6 + 8xy^2 is a 6th degree.

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Multiplying would look like, (4x + 9) (9x + 3), would be 36x + 27

This lesson was learning how to multiply and factor polynomials. This was basically the same as lesson 1 but instead of adding and subtracting it was just multiplying.

To keep it simple, factoring is basically the act of reversing the act of multiplication.

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When factoring you only have to find the GCF like if the equation is (4x^2 + 8y^3 + 16), all you do would be take out the GCF, so 4. Then you have 4(x^2 + 2y^3 + 4), you can't take out anymore, so this is it.

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There is many ways to multiply binomials, them being FOIL, distributive property, a table, and special cases

FOIL stands for First Outers Inners Last and it is quite simple to learn. If you have a equation like (6xy + 18) (3 + 5xy). There are no GCF in this

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Then you would multiply the 6xy by the 3, then you would multiply 18 by the 5xy, then you would multiply the 18 and the 3 and finally you would multiply the 6xy and the 5xy. That would leave you with, (18xy + 90xy)(54 + 30xy)

A table looks like this,

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To factor is basically just reverse multiplication.

If the equation happens to have no GCF then you can use trial and error. In trial and error it's more complicated to do but once you do it a few times it's very easy.

This lesson was about how to factor.

You can find the GCF within a equation by finding the number that all numbers have in common. (2x + 4y^2 - 8) the GCF would be 2

L44 Factoring I: Chapter 8 lesson 4

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This was the same as lesson 44 but we learned how to factor the perfect square trinomial

A perfect square is a number times the same number = something like 7 x7 = 49

L45 Factoring II: Chapter 8 lesson 5