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how do I get from here 2x^3-3x+1 to (x-1)(2x^2+2x-1)

Mathematics
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maybe long division
long division works!
|dw:1347405240429:dw| hopefully you can understand that..

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Other answers:

note at all, I want get from the first one to the second one, say I was given to2x^3-3x+1, how do I get to (x-1)(2x^2+2x-1). I dont see how what you did applies
wait a mistake
there is an alternative way:\[\begin{align} 2x^3-3x+1&=x(2x^2-3)+1\\ &=x(2x^2-3)-(2x^2-3)+(2x^2-3)+1\\ &=(x-1)(2x^2-3)+2x^2-3+1\\ &=(x-1)(2x^2-3)+2x^2-2\\ &=(x-1)(2x^2-3)+2(x^2-1)\\ &=(x-1)(2x^2-3)+2(x-1)(x+1)\\ &=(x-1)(2x^2-3+2(x+1))\\ &=(x-1)(2x^2-3+2x+2)\\ &=(x-1)(2x^2+2x-1) \end{align}\]
this is all to see where 2x^3-3x+1>0
great ty
yw :)
ty also @Mimi_x3

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