All+Together+Now!

media type="youtube" key="jP9j9BysMj8" height="58" width="84"Example: 3x 2 + 2x - 8 > > a = 3 factors: 1 and 3 > > c = -8 factors: 2 and 4 or 1 and 8 >
 * 1) 1 **List the factors of the //a// term and the //c// term**.

> > ( x )( x ) >
 * 1) 2 **Write down two sets of parentheses with empty spaces like this**:

> > (**3**x )(**1**x ) >
 * 1) 3 **Fill the spaces in front of the x's with a pair of possible factors of the //a// value**. There is only one possibility for our example:

>
 * 1) 4 **Fill in the two spaces after the x's with a pair of factors for the constant**. Let's say we choose (3x **8**)(x **1**).

> > If ax 2 + bx + c then (x + h)(x + k) > > If ax 2 - bx - c or ax 2 + bx - c then (x - h)(x + k) > > If ax 2 - bx + c then (x - h)(x - k) > > For our example 3x 2 + 2x - 8 so (x - h)(x + k) > > We'll have to guess as for the rest. (3x + 8)(x - 1) >
 * 1) 5 **Decide what signs should be between the x's and the numbers**. Here's a guide:

> > (3x + 8)(x - 1) > > 3x 2 - 3x + 8x - 8 > > 3x 2 + 5x - 8 ≠ 3x 2 + 2x - 8 >
 * 1) 6 **Test your choice by multiplying (use FOIL) the two parentheses together**. If the middle term is not at least the correct value (disregarding positive or negative) you have chosen the wrong //c// factors.


 * 1) 7 **Swap out your choices if necessary**. In our example, let's try 2 and 4 instead of 1 and 8: (3x + 2)(x - 4)
 * Now our //c// term is an -8.


 * But our Outside/Inside combo is -12x and 2x, which will not combine to make the correct //b// term of +2x.


 * 1) 8 <span style="background-color: #f9f7f1; color: #414141; font-family: Arial,Helvetica,sans-serif; font-size: 14px;">**Reverse the order if necessary**. Let's try moving the 2 and 4 around: (3x + 4)(x - 2)
 * //c// term is still okay.


 * Outside/Inside combo is -6x and 4x. If we combine them, we get pretty close to the 2x we were aiming for --- right amount, wrong sign.


 * 1) <span style="background-color: initial; color: #ffffff; display: block; font-size: 1.45em; text-align: center;">9 <span style="background-color: #f9f7f1; color: #414141; font-family: Arial,Helvetica,sans-serif; font-size: 14px;">**Double-check your signs if necessary**. We're going to stick with the same order, but swap which one has the subtraction: (3x - 4)(x + 2)
 * //c// term is still okay.

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 * Outside/Inside combo is now 6x and -4x. This will combine to create the positive 2x from the original problem, so these are the correct factors.