SOLUTION: Factor the following expression completely: {{{12x^3-18x^2+24x}}}. I have gotten to {{{6x(2x^2-3x+4)}}} but I'm unsure if it can be futher reduced

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor the following expression completely: {{{12x^3-18x^2+24x}}}. I have gotten to {{{6x(2x^2-3x+4)}}} but I'm unsure if it can be futher reduced      Log On


   

Question 290565: Factor the following expression completely: 12x%5E3-18x%5E2%2B24x. I have gotten to 6x%282x%5E2-3x%2B4%29 but I'm unsure if it can be futher reduced
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
12x%5E3-18x%5E2%2B24x. I have gotten to 6x%282x%5E2-3x%2B4%29 but I'm unsure if it can be futher reduced

It cannot. Here is how to tell:

Ax%5E2%2BBx%2BC can be factored if and only if the disriminant
D=B%5E2-4A%2AC is a perfect square.

Consider 2x%5E2-3x%2B4 as Ax%5E2%2BBx%2BC

so that A+=+2, B+=+-3, and C+=+4

Then calculate the discriminant using the formula: 

D=B%5E2-4A%2AC

D=%28-3%29%5E2-4%282%29%2A%284%29

D=9-32

D=-22

Since -22 is not a perfect square, 2x%5E2-3x%2B4
cannot be factored. 

Edwin