Question

And, how to solve 8X^3-12X^2+6X-1=0

Answer 1

if you try grouping them this way \[(8x^3 - 1) - (12x^2 - 6x)\]
then try to factor
\[\implies (2x - 1)(4x^2 + 2x + 1) - 6x(2x - 1)\]
you can see that 2x - 1 is factorable so factor it out
\[\implies (2x-1)(4x^2 + 2x + 1 - 6x)\]
combine like terms
\[\implies (2x-1)(4x^2 - 4x + 1)\]
that second factor is still factorable
\[\implies (2x - 1)(2x-1)^2\]
you can simplify this further
\[\implies (2x-1)^3\]
does that help?

Answer 2

and here is an expansion from wolframalpha that proves \[\large (2x-1)^3 = 8x^3 - 12x^2 + 6x - 1\]

Answer 3

http://www.wolframalpha.com/input/?i=%282x-1%29%5E3

Answer 4

thank you and please help me with 2X^3-5X^2-46X+24=0
I always have the problem to solve the first line like you did my first question.

Answer 5

well you cant use the method i used above to solve this one

Answer 6

you have to solve that the long way

Answer 7

How to do it? Please help me, thanks.

Answer 8

you use long division are you familiar with that?

Answer 9

kind of, but what you divided by?