SOLUTION: I am trying to understand this question in easy terms and an example please. Why do you factor a quadratic equation before you solve? Thank you very much! Regards

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Question 382915: I am trying to understand this question in easy terms and an example please.
Why do you factor a quadratic equation before you solve? Thank you very much!
Regards
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
I am trying to understand this question in easy terms and an example please.
Why do you factor a quadratic equation before you solve? Thank you very much!
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When you have a quadratic problem the "solution" is
immediately seen by any person who can unravel the
pattern expressed by the form. Most people cannot
do that till the quadratic is factored.
---
Example:
When you see x^2+5x+6 = 0 do you "see" the solutions?
Most people do not.
---
So we factor the expression to get:
(x+3)(x+2) = 0
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If you have studied algebra you see the product
is zero so one of the factors must be zero.
---
You say:
x+3 = 0 or x+2=0
Maybe at this point you "see" the solutions.
If not you solve each equation.
x = -3 or x = -2
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Now you have the solutions.
If you had "seen" them in the 1st place you would
not have factored the problem.
----
So, factoring is a crutch we use to help us
"see" the solutions.
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cheers,
Stan H.