Factor
April 17, 2009 
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[phpostock]Factor, 10[/phpostock]
What would be the easiest method to factor out a trinomial equation with exponents raised to the third power?
Question:
I would like to learn a good method to factor out trynomials, one that always works well. Please be as detail and specific as you can.
Let's try this one,
2X ^ 3 - 4X ^ 2 - 30 X = 0
If this one cannot be factored out, is it possible to use the quadratic equations in any form or shape to solve something raised to an odd number such as ^3?
Answer:
the best way for me is the factor theorem
if f(x) is of any higher degree than 2 then I use this
f(a) = 0 then x-a is a factor
in your case - you can factor out an x
x(2x^2-4x-30) = 0
hence
x = 0 or 2x^2-4x-30 = 0 = 2(x^2-2x-15)
x = 0 or 2(x-5)(x+3) = 0
x = 0;5 or -3
if I would have guessed x-1 a factor and worked out f(1) I would not have found 0
____________________________________
My example
lets say
x^3-5x^2-2x+24 = f(x)
now in order to find the factors we can guess
is x-1 a factor? f(1) =1-5-2+24 and not 0
x+1? f(-1) = not 0
f(2) not =0
f(-2) = 0 therefore x+2 is a factor
now you may continue the guessing game or rather use (long)division to find the ploynomial of a lesser grade. Ill try to show with this editor "~" is a space
~~~~~~~~~~~~~~~~x^2~~~-7x +12
~~~~~~~~~~~~~~______________________________
~~~~~~~~~~(x+2)|~~x^3~~-5x^2~~-2x~~~+24
~~~~~~~~~~~~~~~~x^3~~+2x^2
~~~~~~~~~~~~~~~___________
~~~~~~~~~~~~~~~~0 ~~~-7x^2~~-2x
~~~~~~~~~~~~~~~~~~~~-7x^2~-14x
~~~~~~~~~~~~~~~~~~~~~_________
~~~~~~~~~~~~~~~~~~~~~~0 +12x ~~~~+24
~~~~~~~~~~~~~~~~~~~~~~~~~12x~~~~+24
~~~~~~~~~~~~~~~~~~~~~~~~~___________
~~~~~~~~~~~~~~~~~~~~~~~~~~0 ~~~~~0
therefore f(x) =(x^2-7x +12)*(x+2) and I can factorize the 2 nd degree polynomial and I get
f(x) = (x-4)(x-3)(x+2)
just a note - factorization is one of the most difficult things to do with a computer. The genii uses factorization to test quantum computers etc end that is why prime numbers is important.
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