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Find the least common multiple of \(1-x^2\)and \((x-1)^3\). This problem had been bugging me for a bit and I can't figure it out, if someone can help that would be great :)

 Feb 9, 2021
 #1
avatar+116125 
+2

1  - x^2     = ( x - 1)  ( x + 1)   =    -( 1 - x) (x + 1)  =  -( x + 1) ( x  -1)

 

Take the  highest power on each  unique  factor between both  polynomials

 

highest power of  ( x -1)  =  3  =  ( x  -1)^3

highest power of  - (x + 1)  = 1  =   [- (x + 1) ]^1  =  -(x + 1)

 

LCM  =   -(x + 1) ( x - 1)^3

 

 

cool cool cool

 Feb 9, 2021
edited by CPhill  Feb 9, 2021
 #2
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+1

We can rearrange the the first expression as 

$-x^2+1$

we can factor a $-1$

$-1(x^2-1)$

$-(x+1)(x-1)$


the second expression is 

$(x-1)(x-1)(x-1)$

that means

$(x-1)^2*-(x+1)$

 

i am really unsure about the finding the least common multiple, because I am really rusty with that part, but the factoring part is definitely correct 

 Feb 9, 2021
 #3
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+2

Thank you CPhil and Guest! I get it now :)

 Feb 9, 2021

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