SOLUTION: I am learning how to factor equations and am having difficulty with this one.. I can not figure out the GCF to be able to proceed. Not all variables have an X so what do I pull out
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Question 245871: I am learning how to factor equations and am having difficulty with this one.. I can not figure out the GCF to be able to proceed. Not all variables have an X so what do I pull out?
x^3+8x^2+2x+16
Found 2 solutions by solver91311, dabanfield:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Terminology note: 
is NOT an equation. An equation must have an equal sign in it somewhere, and there is no equal sign to be seen here. This is a polynomial expression, specifically a 3rd degree polynomial expression. If this was English class and you claimed that this was a sentence, your teacher would ask "Where is your verb?"
The method illustrated here only works under certain conditions, and in this case those conditions have been contrived by the constructor of the problem. Keep this in your toolbox, but it is not a magic bullet that is always appropriate to use:
Notice that the coefficient on the 
term is 2 times the coefficient on the 
term and the constant term is 2 times the coefficient on the 
term.
Rearrange the terms:
Group the two pairs:
\ +\ \left(8x^2\ +\ 16\right))
Factor from the first group and 8 from the second group:
\ +\ 8\left(x^2\ +\ 2\right))
Now note that the resulting two terms have a factor of 
in common. Factor it out:
\left(x^2\ +\ 2\right))
Since cannot be factored over the real numbers, if factoring over the real numbers is your assignment, then you are done. If you are supposed to consider the complex factors, then:
\left(x\ +\ i\sqrt{2}\right)\left(x\ -\ i\sqrt{2}\right))
John
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
x^3+8x^2+2x+16
Group as follows:
(x^3 + 8x^2) + (2x + 16)
Then factor each grouping as follows:
x^2*(x+8) + 2(x+8) =
(x^2+2)*(x+8)
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