Question

What is the quotient (x3 – 3x2 + 3x – 2) ÷ (x2 – x + 1)?

Answer 1

We need to find the quotient of the given division problem.

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

In order to find its quotient, we will use long division.

$x^{2}-x+1$)$x^{3}-3x^{2}+3x-2$

First of all, we put x in the quotient as $x^{2}$ goes into $x^{3}$, x times.

So, we get:

$x^{2}-x+1$)$x^{3}-3x^{2}+3x-2$(x

$\text{ ..................}x^{3}-x^{2}+x$

Upon subtracting, we get:

$\text{....................}-2x^{2}+2x-2$

We can see that $x^{2}$ goes into $-2x^{2}$, -2 times, therefore, the next term in the quotient will be -2. This makes our quotient as (x-2).

Answer 2

                 x  -   2
              _______________
x^2-x+1 | x^3 - 3x^2 + 3x - 2                x^3 - x^2  +  x                        -------------- 
                       -2x^2 + 2x -2                       -2x^2 + 2x  - 2                       ------------------                                   0
Quotient = x - 2