Question 21453
Factor:
{{{2x^3 - 10x^2 + 12x}}} First, factor 2x from this expression.
{{{2x(x^2 - 5x + 6)}}} Now factor the parentheses. The factors will look like (x - a)(x - b)
What are a and b?  You need (a)(b) = 6 for the constant term and (a)+(b) = -5 for the x-coefficient.
Try: a = -2 and b = -3
(-2)(-3) = 6
(-2)+(-3) = -5
These will work, so the factors are (x - 2)(x - 3).
Putting it all together, we have:
{{{2x^3 - 10x^2 + 12x = 2x(x - 2)(x - 3)}}}