Question 732562
Do you need to do as synthetic division, or is polynomial long division what you want?  Either way, write the dividend in its expanded form:

{{{x^5+0*x^4+3x^3+0*x^2+0*x-6}}}.


{{{x^5+0*x^4+3x^3+0*x^2+0*x-6}}} DIVIDED BY {{{x-1}}}:


X^5/x=^4.  Put this above the x^5 term.
x^4*(x-1)=x^5-1*x^4.  Subtract and obtain 0+x^4.
Bring down next term of dividend, the 3x^3.


x^4/x=x^3.  Put this above the x^4 term of the dividend.
 x^3*(x-1)=x^4-x^3.  Subtract and obtain 0+4x^3.
Bring down next term of dividend, the 0*x^2.


4x^3/x=4x^2.  Put this above the x^3 term of the dividend.
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continue the the steps and process until done.

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Answer quotient will be {{{x^4+x^3+4x^2+4x+5}}} and remainder {{{-1}}}.