Solving a cubic equation by factorization

by Vann
(USA)

Question
Solve this equation: 3x^3 -8x^2 +4x=0

Answer
Solving 3x3 -8x2 +4x = 0 means that we need to find the values of x that satisfy the equation.

Below are the steps to do so:
3x^2-8x^2+4x=0
Notice that, all the terms in this equation have the common factor,x.
x<b>3x^2-8x+4</b>=0

Hence, we can factorize this equation by taking out the common factor, x.Now, on the left hand side, we have a 2 parts, x and the quadratic equation,3x2 -8x +4.

x<b>(3x-2)(x-2)</b>=0
We can factorize the quadratic equation,
3x2 -8x +4
as (3x-2)(x-1).


x(3x-2)(x-2)=0
By doing so, the left hand side is fully factorized and consists of 3 parts. We can now calculate for the values of x.


all parts of x(3x-2)(x-2)  is equals to 0
To calculate for x, since the right hand side of the equation is equals to 0, the left hand side must also equals to 0. For this to be true, any of the 3 parts must be equals to 0.  

x=0
Hence, we have x = 0...

x = 2/3





...3x-2 = 0. Solving this gives
x = 2/3...





x=2
...x -2 = 0. Solving this gives
x = 2...


Therefore, the we have x = 0 or 2/3 or 2.



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