Question

Divide (long division) the polynomial by the accompanying linear expression:x^3+x^2−2x+3, x−1

Answer 1

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 :

$\begin{gathered} x^3+x^2−2x+3 \\ -(x^3-x^2) \\ ---------- \\ 0+2x^2-2x+3 \end{gathered}$

Find another expression to cancel the new first term:

(x-1)*(2x)=2x^2-2x

Subtract :

$\begin{gathered} 2x^2-2x+3 \\ -(2x^2-2x) \\ -------------- \\ 0+0+3 \end{gathered}$

Hence, the whole answer is given by the terms that we found(quotients) plus the remainder over the dividend.

$=x^2+2x+\frac{3}{x-1}$