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a, b, c deben dar -3 al multiplicarse. Probemos con
a=3
b=1
b=-1
(x+a)(x+b)(x+c) = (x+3)(x+1)(x-1) = (x²+4x+3)(x-1) =
x³+4x²+3x-x²-4x-3 = x³+3x²-x-3 ≠ x³+23x/6+3x/2-3
Probemos ahora con
a=3
b=3/2
c=-2/3
(x+a)(x+b)(x+c) = (x+3)(x+3/2)(x-2/3) = (x²+9x/2+9/2)(x-2/3) =
x³+9x²/2+9x/2-2x²/3-18x/6-18/6 = x³+23x²/6+9x/6-3 =
x³+23x²/6+3x/2-3
Por lo tanto:
6x³+23x²+9x-18 = x³+23x/6+3x/2-3 = (x+3)(x+3/2)(x-2/3)