Question 199198
You certainly can use synthetic division to solve this problem. Whether you use synthetic division or long division you get the same answer of: {{{highlight(x^3+3x^2+3x+1)}}} with a remainder of zero.  This means that the divisor {{{x+1}}} is a factor of {{{x^4+4x^3+6x^2+4x+1}}}.
The answer is not, as you have writen, {{{(x^3+3x^2+3x+1)/highlight_green((x+1))}}}