Hello
I came across a question in my math textbook that i am confused by.
Below is the question.
[imath]2(x-1)^3=32[/imath]
initially i tried collecting everything to one side, expanding all the terms and then factorizing the new cubic polynomial using the factor theorem and rational root theorem, however i found that this did not work when i tried it as none of the possible values values i got from using the rational root theorem made the equation equal 0. I then took the simpler approach of dividing both sides by 2, cube rooting the right side and then add 1 to the right side, this worked.
What i am asking is why did my first approach not work. below is a picture of my first approach. All help appreciated.
![20240814_213505.jpg 20240814_213505.jpg](https://www.freemathhelp.com/forum/data/attachments/35/35779-c7f8dd0d3b293e554f84c15735335ec0.jpg)
I came across a question in my math textbook that i am confused by.
Below is the question.
[imath]2(x-1)^3=32[/imath]
initially i tried collecting everything to one side, expanding all the terms and then factorizing the new cubic polynomial using the factor theorem and rational root theorem, however i found that this did not work when i tried it as none of the possible values values i got from using the rational root theorem made the equation equal 0. I then took the simpler approach of dividing both sides by 2, cube rooting the right side and then add 1 to the right side, this worked.
What i am asking is why did my first approach not work. below is a picture of my first approach. All help appreciated.
![20240814_213505.jpg 20240814_213505.jpg](https://www.freemathhelp.com/forum/data/attachments/35/35779-c7f8dd0d3b293e554f84c15735335ec0.jpg)