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Kharel's Simple Procedure for Factoring Quadratic Equations

The general form for quadratic equations is:
 
Ax2+Bx+C
 
If A=1, you have x2+Bx+C=0, and the following procedure always works.
If A ≠ 1, then Step 1 of both Scenarios below will always apply, but not Step 2.
 
The general form of the factors in this case will look like:
 
(x + D)*(x + E)
 
where D and E are factors of C whose sum is B.
 
In order to find D and E, its important to know whether they are positive or negative first.
We find this out by using a simple procedure.
 
Scenario #1:
Step 1:
If C is negative:
We know that D is positive and E is negative (or vice versa, it doesn't really matter which order you choose).
 
Step 2:
If B is positive, we know that the factor of C with the larger absolute value will be the positive number.
If B is negative, we know that the factor of C with the larger absolute value will be the negative number.
 
Scenario #2:
 
Step 1:
If C is positive:
We know that D and E are both the same sign, either both positive or both negative.
 
Step 2:
If B is positive, C and D are both positive.
If B is negative, C and D are both negative.
 
Once you've figured out the signs (positive or negative) for D and E, then all that's left is the simple job of finding a pair of factors of C that add up together to equal B. In other words, D*E = C and D+E = B.
 
After that, you're done and you've successfully factored your quadratic equation. Congratulations. Now try this procedure on a few practice problems to prove it works and become comfortable with using it. It'll save you hours.
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Kharel T.

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