Pd+2

Below is the list of who is responsible for which topics to summarize:
====(All topics are due 2 cycles after the date topic was taught in class) ====




5-4- Ryan, Katelyn
==== __Factoring Polynomials:__ Ex 1: **Factoring **  - Factoring is the opposite of multiplication. When you factor, try to look for the GCF between all of the ==== ====terms in the problem Ex: 4y^2 - 8. Step 1 - In this example, 4 is the GCF, so we pull it out of the problem and write it as a product of the factors. ==== ====4y ^2  - (4)2 Step 2 : Next we will rewrite the equation using the distributive rule of multiplying (a(b + c) = ab + ac) Final outcome - **4(y^2****- 2)** ==== ====Ex 2: <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;">**<span style="font-family: 'Times New Roman',Times,serif;">Multiplication ** <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;"> - The multiplication of polynomials allows someone to factor polynomials by multiplying polynomials together in order to factor ==== ====<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">the problem --- <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;">**<span style="font-family: 'Times New Roman',Times,serif;">FOIL (Front-Outer-Inner-Last) Method : (x+3)(x+4) ** <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;"> <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;">//<span style="font-family: 'Times New Roman',Times,serif;">Step 1 // <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">: Multiply the first two polynomials in each pair (X and X), this ==== ====<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">gives us x^2 <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;"><span style="font-family: 'Times New Roman',Times,serif;"> //<span style="font-family: 'Times New Roman',Times,serif;">Step 2 // <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">: Multiply the outer two polynomials in each pair (X and 4), this gives us 4x <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;">//<span style="font-family: 'Times New Roman',Times,serif;">Step 3 // <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">: Multiply the inner two polynomials in each ==== ====<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">pair (3 and x) this gives us 3x <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;"><span style="font-family: 'Times New Roman',Times,serif;"> //<span style="font-family: 'Times New Roman',Times,serif;">Step 4 // <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">: Multiply the last two polynomials in each pair (3 and 4), this gives us 12 <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;">//<span style="font-family: 'Times New Roman',Times,serif;">Step 5 // <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">: Combine like terms : ==== ====<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">x^2+ <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;">**<span style="font-family: 'Times New Roman',Times,serif;">4x+3x ** <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">+12 <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;">//<span style="font-family: 'Times New Roman',Times,serif;">Step 6 // <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: 'Times New Roman',Times,serif; font-size: 15px; line-height: 20px; white-space: normal;">: Solve : <span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; font-family: arial,helvetica,sans-serif; font-size: 15px; line-height: 20px; white-space: normal;">**<span style="font-family: 'Times New Roman',Times,serif;">x^2+7x+12 ** <span style="font-family: 'Times New Roman',Times,serif; font-size: 15px;"> --- **Multiplying Polynomials** - This method is for multiplying larger factoring equations ====

Ex: **(**//**x**// **+ 3)(**//**x^2**// **-** **2**//**x**// **+ 4)**
//Step 1 :// ( // x // ) // x^2 // - ( // x // ) 2//x// + ( // x // ) 3 + (3) // x^2 // - (3) 2//x// + (3) 4 //Step 2:// //x^2// - 2//x^2// + 3//x// + 3// x^2 // - 6//x// + 12 Answer **:**//**x^3**// <span style="color: #000000; font-family: 'Times New Roman',Times,serif;">**-3x^2-** //**x**// **+ 12** ====<span style="-webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; color: #000000; font-family: arial,helvetica,sans-serif; font-size: 15px; font-weight: normal; line-height: 20px; white-space: normal;"> ====

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