Question

What is the result when x^3 - 3x^2 + 3x - 1 is divided by x - 1

Answer 1

We have to find a second degree equation , which multiplied by (x-1) gives the polynomial equation.
( ax^2 + bx +c) * ( x-1) = x^3 - 3x^2 + 3 x -1
ax^3 +bx^2 + cx - ax^2 -bx -c = x^3 -3x^2 +3x -1
Then,
a =1
b- a = -3 ,b = -2
c = 1
-b +c = 3 , b= -2
The equation will be : x^2 -2x +1

Answer 2

Using Synthetic division with coefficients as shown below:

We get the coefficients for the quotient as 1, -2, & 1 which means the quotient is x^2 - 2x + 1 = 0.