Question 925084
{{{(x-1)^2=x^2-2x+1}}},  the square because multiplicity 2.

Perform the division, polynomial division.  You must include the term for x^3 in the dividend.


_________________|________3x^2__+6x____-45__________________Quotient Line
______________________________________________
x^2-2x+1_________|________3x^4+0*x^3-54x^2+96x-45
__________________________3x^4-6x^3+ 3x^2
_____________________________0+6x^3-57x^2+96x
_______________________________6x^3-12x^2+6x
________________________________0__-45x^2+90x-45
___________________________________-45x^2+90x-45
_________________________________________________
__________________________________________0+0+0_________Remainder 0



The quotient has a scalar factor, so although factoring not yet complete, you know you have  {{{(x-1)^2*3*(x^2+2x-15)}}}; which you can finish into
{{{highlight(3(x-1)^2(x-3)(x+5))}}}.