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I'm studying for the accuplacer exam and I can't wrap my head around how to find the values in a cubed polynomial.

The example i'm having trouble with is: $27x^3 = 1$

The answers are $1/3$ and $(-1 \pm i \sqrt3 ) / 6$

I have absolutely NO clue how to solve this problem.. other than at some point I obviously have to use the quadratic formula. Thanks for any help you can offer.

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1 Answer

up vote 3 down vote accepted

Hint :

$27x^3-1^3=(3x)^3-1^3=(3x-1)(9x^2+3x+1)$

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Thank you, how did you get from 27x^3 to (3x)^3? –  simon Apr 16 '12 at 5:39
    
never-mind.. i'm an idiot. –  simon Apr 16 '12 at 5:40
    
@simon $27=3^3$ –  pedja Apr 16 '12 at 5:40
    
Alright so really i just completely forgot about the sum/difference of two cubes formulas.. ug remembering old math is hard. Any tips on how to memorize those? –  simon Apr 16 '12 at 5:49
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The way to memorize formulas is to use them so much that you get past the point where you have to look them up. Or, as the New Yorker told the tourist who asked how to get to Carnegie Hall, practice, practice, practice. –  Gerry Myerson Apr 16 '12 at 5:52
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