contestada

which of the following expressions is this one equivalent to?
(x^4-2x^3+x-2) ÷ (x^3+1)
A. x^2-x+1
B. x^2+1
C. x-2
D. x^2+3x+2

Respuesta :

cryssatemp

Answer: C. x-2

Step-by-step explanation:

We have the following expression:

[tex]\frac{x^{4} -2x^{3} +x-2}{x^{3}+1}[/tex]

Factoring in the numerator:

[tex]\frac{x(x^{3}+1)-2(x^{3}+1)}{x^{3}+1}[/tex]

Factoring again in the numerator with common factor [tex]x^{3}+1[/tex]:

[tex]\frac{(x^{3}+1)(x-2)}{x^{3}+1}[/tex]

Simplifying:

[tex]x-2[/tex]

Hence, the correct option is C. x-2

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