Lesson Factoring trinomials: SHORTCUT!!!

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Normal style of factoring would take many trials and errors, so I prefer this method:

Here's the shortcut in factoring general <A HREF=Trinomial.wikipedia>trinomials</A> with the format {{{ax^2+bx+c=0}}}

Solve for x as if {{{ax^2+bx+c=0}}} and consequently you may opt to use the <A HREF=/algebra/homework/quadratic/>QUADRATIC FORMULA</A>!!!

There you would find two roots: say y and z

Then,

{{{x=y}}} or {{{x=z}}}

{{{x-y=0}}} or {{{x-z=0}}}

Here, {{{x-y}}} and {{{x-z}}} are the factors.

So, {{{ax^2+bx+c = (x-y)(x-z)}}}.

NOTE: {{{ax^2+bx+c}}} is considered PRIME or not factorable if y and z are imaginary.

EXTENSION!!!

But, if the answer is rational and is not an integer, see below

If the roots are {{{x=9/2}}} and {{{x=3/4}}}

{{{x=9/2}}}
{{{2x=2(9/2)}}}
{{{2x=9}}}
{{{2x-9=0}}}----------------this is the first factor

{{{x=3/4}}}
{{{3x=4}}}
{{{3x-4=0}}}----------------this is the other factor!
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