SOLUTION: Hello. I'm needing some help factoring out this trinomial. a^6-2+a^3 thanks!

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Question 184677: Hello.
I'm needing some help factoring out this trinomial.
a^6-2+a^3
thanks!
Found 2 solutions by josmiceli, solver91311:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E6++-+2+%2B+a%5E3
a%5E6+%2B+a%5E3+-+2
Make this substitution:
z+=+a%5E3
Then change the expression to:
z%5E2+%2B+z+-+2
By inspection, I see:
%28z+%2B+2%29%28z+-+1%29
Now substitute again
%28a%5E3+%2B+2%29%28a%5E3+-+1%29 answer

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Let then



But since



But is the difference of two cubes, so since:



We can say:




If you are factoring over the rational numbers then the complete factorization is:



However, if you are allowed to consider irrational factors you could also say:






John