We need to divide the next polynomial x^3+x^2−2x+3 by x-1.
First, we need to find an expression to cancel the firs term:
(x-1)*(x^2)= x^3 - x^2
Subtract :
[tex]\begin{gathered} x^3+x^2−2x+3 \\ -(x^3-x^2) \\ ---------- \\ 0+2x^2-2x+3 \end{gathered}[/tex]Find another expression to cancel the new first term:
(x-1)*(2x)=2x^2-2x
Subtract :
[tex]\begin{gathered} 2x^2-2x+3 \\ -(2x^2-2x) \\ -------------- \\ 0+0+3 \end{gathered}[/tex]Hence, the whole answer is given by the terms that we found(quotients) plus the remainder over the dividend.
[tex]=x^2+2x+\frac{3}{x-1}[/tex]