Difference between revisions of "Factoring Quadratics"
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=== Limitations === | === Limitations === | ||
| − | None known. | + | None currently known. |
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== Also See == | == Also See == | ||
* [[Quadratic equation]] | * [[Quadratic equation]] | ||
* [[Factoring]] | * [[Factoring]] | ||
* [[Vieta's Formulas]] | * [[Vieta's Formulas]] | ||
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| + | [[Category:Algebra]] | ||
| + | [[Category:Quadratic equations]] | ||
Latest revision as of 17:13, 9 August 2024
The purpose of factoring a quadratic is to turn the quadratic into a product of 2 binomials.
Method 1
Method 1 starts with factoring the product of the roots. Let the quadratic we are factoring be 
. When factored, it will be in the form of ![\[a(x-r)(x-s)=0,\]](http://latex.artofproblemsolving.com/e/c/8/ec86197d724becc0abcb624e98f7869d17200e2c.png)
where 
and 
are the roots of the quadratic, and where 
and 
.
Example
Since the coefficient on the 
term is 
, we know are quadratic factors in the form of 
. We know that the factor pairs of 12 are 
and 
We can find that only 
and 
satisfy our equations and , so the factored form of is 
.
Limitations
This method cannot be used to factor quadratics with complex or irrational roots.
Method 2
Method 2 starts by using the sum. Let the quadratic we are factoring be . When factored, it will be in the form of where and are the roots of the quadratic, and where and .
Example
We know that 
, so we can set 
and 
. Then, we get that 
, giving us that 
, or 
. Because we have both 
and 
as our roots, it doesn't matter which one is plugged in, giving us that the factored form of is 
.
Limitations
None currently known.
