Polynomial Question

by Sketch

(x^3) = (3x^2)
(x^3)/(x^2) = 3
x = 3

My maths teacher told me this move isn't 'allowed' yet I've done this several times and produced the correct answer. Why is this not allowed?

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Polynomial Question

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Jul 18, 2011
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by: Anonymous

Hi Sketch,

The reason you can't use this method is because you are trying to solve a polynomial. There are very specific methods for solving polynomials that you must adhere to. A polynomial often has more than one answer. With your method, you've only found one of the two answers.

For this problem, I would start by subtracting 3x^2 from both sides to set the equation equal to 0. This way, you'll be able to factor the equation.

x^3 - 3x^2 = 3x^2 - 3x^2
x^3 - 3x^2 = 0

Now we can factor using the GCF. We can factor out x^2.

x^2(x-3) = 0

Now we can set each factor equal to 0 using the Zero Product Property.

x^2 = 0 and x - 3 = 0

x = 0 and x = 3

We have two solutions to this polynomial:

x = 0 and x = 3.

I hope this helps!

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