Question 290565
{{{12x^3-18x^2+24x}}}. I have gotten to {{{6x(2x^2-3x+4)}}} but I'm unsure if it can be futher reduced
<pre><font size=4 color = "indigo"><b>
It cannot. Here is how to tell:

{{{Ax^2+Bx+C}}} can be factored if and only if the disriminant
{{{D=B^2-4A*C}}} is a perfect square.

Consider {{{2x^2-3x+4}}} as {{{Ax^2+Bx+C}}}

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

Then calculate the discriminant using the formula: 

{{{D=B^2-4A*C}}}

{{{D=(-3)^2-4(2)*(4)}}}

{{{D=9-32}}}

{{{D=-22}}}

Since -22 is not a perfect square, {{{2x^2-3x+4}}}
cannot be factored. 

Edwin</pre>