Difference between revisions of "Factoring Quadratics"
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Latest revision as of 18:13, 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
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.