A Very Nice Math Olympiad Question | How to solve x^2-x^3=12 | Algebra

See the way I breakdown the solution of this question. There is a lot you can learn from this video.
How to solve x^2-x^3=12. ENJOY

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[cyruschang]

x^2 - x^3 = 12
x^3 - x^2 + 12 = 0
(x + 2)(x^2 - 3x + 6) = 0
x = -2, (3 +/- i✓15)/2

[Kube-Themathsolver]

it was really a good video. it was intuitive and simple

[Adam-lxmt]

Nice use of some algebraic identities. Personally, I think it would be more straightforward to solve by guessing the x=-2 solution and then algebraic long division (or comparing coefficients method).

[harrymatabal]

Excellent. I would have used remainder and factor theorem

[pjaj]

Most of these questions only want integer solutions.
x^2 - x^3 = 12
x^2 * (1 - x) = x * x * (1 - x) = 2 * 2 * 3 but also -2 * -2 * 3
by comparison of terms x = -2

[Sus-dp]

I solved that in like 15 seconds. I started at going through possible numbers and started at 2 since 1-1=0, I knew 2^2=4 and 2^3=8 which add to 12. I knew I was on the right track. So i used -2 as x and it worked

[sandytanner]

Divide by x+2 and we get also x^2-3x+6=0 (besides x+2=0)

[МихаилШа-чю]

Why won’t you use quadratic formula from the start?

[gamingwithhjp]

This is a good video, easily understandable and simple . Keep the good work

[esktw]

couldnt we have made out the answer from x^2 + x^3 = 2^2 + 2^3

[ARV]

Sir, the letters very small and unable to identify easily. Please make them larger.