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x3 + 3x2 - 6x - 8 = (x - 2)(x2 + 5x + 4) = (x - 2)(x + 1)(x + 4)
x3 - 3x2 + x - 3 = (x2 +1)( x - 3)
3x2 - 5x - 2 can be factored into (3x + 1) (x - 2)
[ x3 + 3x2 + 2x ] is a trinomial. It's factors are [ x, (x + 1), (x + 2) ] .
I will use the quotient rule here. d/dx(f(x)/g(x) = g(x)*f'(x) - f(x)*g'(x)/[g(x)]2 x3*1/x - ln(x)*3x2/(x3)2 x3/x - 3ln(x)x2/x6 x2 - 3ln(x)x2/x6 = - 3ln(x)/x4 =========