SOLUTION: 2y^6 - 128
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Question 351646: 2y^6 - 128
Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
Hi,
If I am understanding the question properly
.
.
.
y = 2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Presumeably you want a complete factorization of this 6th degree polynomial expression.
Let 
.
Then
Take out a 2:
)
Factor the quadratic binomial:
\left(u\ +\ 8\right))
Replace the substitution:
\left(y^3\ +\ 8\right))
Use the sum and difference of cubes factorization:
\left(y^2\ +\ 2y\ +\ 4\right)\left(y\ +\ 2\right)\left(y^2\ -\ 2y\ +\ 4\right))
If you are factoring over 
, then you are done. If you need to factor over 
, then continue using the quadratic formula to determine the four complex factors (verification left as an exercise for the student):
\left(y\ +\ 1\ -\ i\sqrt{3}\right)\left(y\ +\ 1\ +\ i\sqrt{3}\right)\left(y\ +\ 2\right)\left(y\ -\ 1\ -\ i\sqrt{3}\right)\left(y\ -\ 1\ +\ i\sqrt{3}\right))
Ending with 6 binomial factors as the Fundamental Theorem of Algebra guarantees for a 6th degree polynomial.
John
My calculator said it, I believe it, that settles it
