Factoring



**Topic Overview:**
Have you been having problems with factoring? If you have, then here are some equations that will hopefully help you understand factoring more. **Equations:** **x^2+bx+c and Ax^2+bx+c <--- Both of these equations deal with factoring Trinomials **

  
 * Previous information from: Prentice Hall Mathematics, Algebra I, North Carolina Adopted Edition, 2004 **


 <span style="color: rgb(0, 255, 0)"><span style="color: rgb(0, 255, 0)"><span style="color: rgb(246, 96, 0)">**1. Factoring Checklist:** <span style="color: rgb(255, 0, 153)">**Two Terms:** <span style="color: rgb(153, 0, 170)"><span style="color: rgb(0, 255, 0)">**GCF:** <span style="color: rgb(255, 0, 0)"><span style="color: rgb(255, 34, 102)"><span style="color: rgb(255, 0, 85)"> <span style="color: rgb(255, 34, 102)">  <span style="color: rgb(255, 0, 102)"><span style="color: rgb(255, 34, 102)">**Ex:**  2x^4+6x=2x(x^3+3) <span style="color: rgb(0, 255, 0)">**Difference of Squares:** <span style="color: rgb(255, 0, 102)"><span style="color: rgb(255, 0, 85)">**Ex:** x^2-25= (x+5)(x-5) <span style="color: rgb(153, 0, 170)"><span style="color: rgb(0, 255, 0)">**GCF:** <span style="color: rgb(255, 0, 85)">**Ex:** x^3+x^2+x= x(x^2+x+1) <span style="color: rgb(0, 255, 0)">**(x^2) Make Two Groups:** <span style="color: rgb(255, 0, 85)">**Ex:** x^2+5x+6 -->(x+3)(x+2) <span style="color: rgb(0, 255, 0)">**(ax^2) Slide n' Divide:** <span style="color: rgb(255, 0, 85)">**Ex:** 3x^2+x-2-->x^2+x-6= (x+3/3)(x-2/3)-->(x+1)(3x-2) <span style="color: rgb(255, 0, 153)"> <span style="color: rgb(153, 0, 204)"><span style="color: rgb(153, 0, 170)"><span style="color: rgb(0, 255, 0)">**GCF:** <span style="color: rgb(255, 0, 85)">**Ex:** 3x^2+x-2-->x^2+x-6= (x+3)(x-2)-->(x+3/3)(x-2/3)-->(x+1)(3x-2) <span style="color: rgb(0, 255, 0)">**Grouping:** <span style="color: rgb(255, 0, 85)">**Ex:** <span style="color: rgb(153, 0, 255)"><span style="color: rgb(153, 0, 255)"><span style="color: rgb(153, 0, 204)">(6xy^2-3xy)+(8y-4)-->3xy(2y-1)+4(2y-1)-->(3xy+4)(2y-1 )   <span style="color: rgb(246, 96, 0)"><span style="color: rgb(255, 0, 153)"><span style="color: rgb(153, 0, 255)"><span style="color: rgb(255, 0, 85)"> <span style="color: rgb(153, 0, 255)">g^2+7g+10= (g+2)(g+5)     <span style="color: rgb(204, 0, 238)"> <span style="color: rgb(246, 96, 0)"> <span style="color: rgb(153, 0, 255)">**<span style="color: rgb(255, 0, 153)">Ex: ** <span style="color: rgb(153, 0, 255)"> 6y^2 - 24---> 6(y^2 - 4)= 6(y + 2)(y - 2) <span style="color: rgb(246, 96, 0)"> <span style="color: rgb(255, 0, 153)">**Equation: x^2+bx+c <---(without coefficients) Ax^2+bx+c <---(without coefficients)<span style="color: rgb(255, 0, 85)"> Ex: (without coefficient)---> ** <span style="color: rgb(246, 96, 0)"><span style="color: rgb(255, 0, 153)"><span style="color: rgb(153, 0, 255)"><span style="color: rgb(255, 0, 85)"><span style="color: rgb(153, 0, 255)">g^2+7g+10= (g+2)(g+5)     <span style="color: rgb(246, 96, 0)"><span style="color: rgb(255, 0, 153)"><span style="color: rgb(153, 0, 255)"><span style="color: rgb(255, 0, 85)"><span style="color: rgb(153, 0, 255)"> <span style="color: rgb(255, 0, 85)">**Ex: (with coefficient)--->** <span style="color: rgb(153, 0, 255)">5x^2+13x-6 -->x^2+13x-30= (x+15)(x-2)-->(x+15/5)(x-2/5)-->(x+3)(5x-2) <span style="color: rgb(246, 96, 0)"> <span style="color: rgb(255, 0, 153)">**Previous information from: Study Guide &Workbook, Prentice Hall Mathematics, Algebra I**
 * <span style="color: rgb(255, 0, 153)">Three Terms: **
 * Four Terms:**
 * 2. Factoring Binomials:**
 * 3. Factoring Trinomials with and without coefficients in front of x^2:**
 * 4. Factoring Polynomials with Four Terms:**
 * <span style="color: rgb(255, 0, 85)">Ex: ** <span style="color: rgb(153, 0, 255)">2x^3-8x^2+5x-20= (2x^3-8^2)+(5x-20)--->2x^2(x-4)+5(x-4)--->(2x^2+5)(x-4)


 * 5. Solving Quadratic Equations by Factoring:**
 * <span style="color: rgb(255, 0, 85)"> Ex: ** <span style="color: rgb(153, 0, 255)">x^2+5x+6=0= (x+2)(x+3)---> (x+2)(x+3)=0---> x+2=0 or x+3=0---> x=-2,-3
 * <span style="color: rgb(255, 0, 153)">Previous information from: http://www.purplemath.com/modules/solvquad.html**

<span style="font-family: Arial,Helvetica,sans-serif"><span style="color: rgb(0, 153, 238)">Word Problem:
An object is launched at <span style="color: rgb(153, 0, 255)">19.6 <span style="color: rgb(153, 0, 255)"> meters per second (m/s) from a <span style="color: rgb(153, 0, 255)">58.8 <span style="color: rgb(153, 0, 255)">-meter tall platform. The equation for the object's height <span style="color: rgb(153, 0, 255)">//s// <span style="color: rgb(153, 0, 255)"> at time <span style="color: rgb(153, 0, 255)">//t// <span style="color: rgb(153, 0, 255)"> seconds after launch is <span style="color: rgb(153, 0, 255)">//s//(//t//) = –4.9//t//2 + 19.6//t// + 58.8 <span style="color: rgb(153, 0, 255)">, where <span style="color: rgb(153, 0, 255)">//s// <span style="color: rgb(153, 0, 255)"> is in meters. When does the object strike the ground? ** <span style="color: rgb(0, 255, 0)"><span style="color: rgb(0, 255, 0)"><span style="color: rgb(153, 255, 0)"><span style="color: rgb(153, 0, 255)">**<span style="color: rgb(0, 255, 0)"> 0= -4.9t^2+19.6t+58.8 0= t^2-4t-12 0= (t-6)(t+2) Extraneous Solution: Ignore "t= -2" because negative time doesn't work in this problem. The ball strikes the ground six seconds after launch. <span style="color: rgb(255, 0, 153)">Previous information from: ** **http://www.purplemath.com/modules/quadprob.html**
 * <span style="color: rgb(153, 0, 255)">

**<span style="font-family: Arial,Helvetica,sans-serif"><span style="color: rgb(0, 153, 238)">Two Additional Links: **
http://www.factoring-polynomials.com/ **<span style="color: rgb(255, 0, 153)">**^--- These websites are very helpful, especially if you want to explore more sites to learn more about factoring. : ]** <span style="color: rgb(0, 153, 238)">
 * http://www.purplemath.com/index.html <span style="color: rgb(255, 0, 153)"><span style="color: rgb(255, 0, 153)">


 * C<span style="color: rgb(153, 0, 255)">r <span style="color: rgb(0, 255, 0)">e <span style="color: rgb(255, 153, 0)">a <span style="color: rgb(255, 0, 85)">t <span style="color: rgb(255, 0, 153)">e d <span style="color: rgb(153, 0, 255)">b <span style="color: rgb(0, 255, 0)">y : <span style="color: rgb(255, 153, 0)">C <span style="color: rgb(255, 0, 85)">a <span style="color: rgb(255, 0, 153)">r o<span style="color: rgb(153, 0, 255)">l <span style="color: rgb(0, 255, 0)">i <span style="color: rgb(255, 153, 0)">n <span style="color: rgb(255, 0, 85)">a <span style="color: rgb(255, 0, 153)">P a<span style="color: rgb(153, 0, 255)">e <span style="color: rgb(0, 255, 0)">z ** **<span style="color: rgb(255, 153, 0)">: <span style="color: rgb(255, 0, 85)">] **