Question

What is the remainder when (x3 + 1) is divided by (x2 – x + 1)?

A. x+1
B. x
C. 2
D. 0

Answer 1

Answer: x+1

Explanation:

(x^3+1)/(x^2-x+1)

Factor the expression

= (x+1)(x^2-x+1) / (x^2-x+1)

= x+1

Answer 2

x+1

Explanation:

x^3 +1 is the sum of cubes

We can factor this into

(a^2 +b^2 ) = (a+b) ( a^2 -ab+b^2)

(x^3+1) = (x+1)(x^2 -1x+1^2)

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

(x^3+1) / (x^2 -1x+1^2)

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

(x+1)