Factoring Quadratics
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 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 known.