6x^2 - 24x^3 + 36x becomes easier to factor if you notice that 6x is a factor of all 3 terms. Factoring, we get 6x(x - 4x^2 + 6), or -6x(4x^2 - x + 6).
To factor 4x^2 - x + 6, I'd choose from one of the following approaches: quadratic formula, factoring using synthetic division.
Quadratic formula:
1 plus or minus sqrt( 1 - 4(4)(6) )
x = -----------------------------------------------
8
1 plus or minus sqrt(-95)
= ------------------------------------
8
Then the desired factors are complex:
(6) (x - [1 plus sqrt(95] ) (x - [1 minus sqrt(95) ] )
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8
