we are given
[tex]\frac{2x^5-x^4+3x^2-x+5}{x-1}[/tex]
Here , we have
[tex]dividend=2x^5-x^4+3x^2-x+5[/tex]
[tex]divisor=x-1[/tex]
now, we can use synthetic division
so, we get
[tex]Quotient=2x^4+x^3+x^2+4x+3[/tex]
[tex]Remainder=8[/tex]
now, we can write in fraction form
[tex]\frac{2x^5+x^4+3x^2-x+5}{x-1}=(2x^4+x^3+x^2+4x+3)+\frac{8}{x-1}[/tex]............Answer
