SOLUTION: factor 25g^6 -10g^3 +1

Question 635912: factor 25g^6 -10g^3 +1
Found 3 solutions by DrBeeee, lwsshak3, Alan3354:
Answer by DrBeeee(684)   (Show Source): You can put this solution on YOUR website!
Let x = g^3
your expression becomes 25x^2 - 10x + 1 which factors into (5x-1)(5x-1) or
(5x-1)^2
In terms of g we have (5g^3 - 1)^2

Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
factor 25g^6 -10g^3 +1
set equation=0
25g^6 -10g^3 +1=0
let u=g^3
u^2=g^6
..
25u^2-10u+1=0
(5u-1)(5u-1)=0
u=1/5 (multiplicity 2)
u=1/5=g^3
raise both sides to 1/3 power or take cube root of both sides
g=5^(-1/3)
g≈0.5848...
two factors are: irrational number 0.5848...(multiplicity 2)
The other four factors are 2 pairs of non-real or imaginary numbers)
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
factor 25g^6 -10g^3 +1
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When both ends are perfect squares, check that first.

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