SOLUTION: Hello.
I'm needing some help factoring out this trinomial.
a^6-2+a^3
thanks!
Algebra.Com
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) (Show Source): You can put this solution on YOUR website!
Make this substitution:
Then change the expression to:
By inspection, I see:
Now substitute again
answer
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
then
(x - 1))
But since
(x - 1) = (a^3 + 2)(a^3 - 1))
But 
is the difference of two cubes, so since:
(x^2 \mp xy + y^2))
We can say:
(a^2 + a + 1))
If you are factoring over the rational numbers then the complete factorization is:
(a - 1)(a^2 + a + 1))
However, if you are allowed to consider irrational factors you could also say:
(a^2 - a\cdot 2^{\frac{1}{3}} + 2^{\frac{2}{3}})(a - 1)(a^2 + a + 1))
John
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