Question

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

x – 2

x + 2

x – 4

x + 1

Answer 1

A x-2

Explanation:

Equation: (x3 – 3x2 + 3x – 2) ÷ (x2 – x + 1)

Work:

(x3 – 3x2 + 3x – 2) ÷ (x2 – x + 1)

(x^2 - x + 1)(x - 2) over x^2 - x + 1

x - 2

Final Answer:

x - 2

Answer 2

x3 - 2x2 - x
`(x^(3) - 3x^(2) + 3x - 2)/(x^(2) - x + 1) = (x^(3) - 2x^(2) - x^(2) + 2x + x - 2)/(x^(2) - x + 1) = (x^(2)(x) - x^(2)(2) - x(x) + x(2) + 1(x) - 1(2))/(x^(2) - x + 1) = (x^(2)(x - 2) - x(x - 2) - 1(x - 2))/(x^(2) - x + 1) = ((x^(2) - x + 1)(x - 2))/(x^(2) - x + 1) = x - 2`

The answer is A.