Volume with Factoring Cubic Equations SAT ACT Prep

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This question practices a lot of different concepts such as volume, factoring, and solving a cubic equation. I know you can probably solve it faster but I just want to review some major concepts.

0:00 Writing the Equation
1:07 Solving the Equation
  1. Mathodman
  2. cubic equations
  3. solving cubic equations
  4. cubic function
  5. factoring cubic functions
  6. factoring cubic equations
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Hi again !

Your solution is very nice !!!
But in my opinion it's a bit over the top for a question in this level.
Actually, in this particular question, you can (and should) divide by 2x !!!

We know that x can't be 0 in any case, because length is always a positive value.

So we don't really care if we lose this solution - It's irrelevant anyway (also we can see that 0 doesn't appear as a possible answer).

After dividing by 2x, we get a simple quadraric equation, that is easier and faster to solve.

Always remember - It's SAT exam !!!
The state of mind that should be guiding us, is "How can we shorten the solving methods in order to get to the answer as fast as possible".

Thanks !

Ben-El_Musayov