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 :)

TC072 Feb 9, 2021

#1**+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

CPhill Feb 9, 2021

#2**+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

Guest Feb 9, 2021