Question

Which of the following expressions is this one equivalent to?

Answer 1

Answer: C. x-2

Step-by-step explanation:

We have the following expression:

$\frac{x^{4} -2x^{3} +x-2}{x^{3}+1}$

Factoring in the numerator:

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

Factoring again in the numerator with common factor $x^{3}+1$:

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

Simplifying:

$x-2$

Hence, the correct option is C. x-2