Question

Which of the following expressions is this one equivalent to?

(x^4+2x^3-x-2)÷(x^3-1)

A. 2x-5- (3/x^3-1)
B. x^2+x+1
C. x+2
D. x^2+3x+2
...?

Answer 1

Answer: x+2. The answer is C.

Explanation:

Answer 2

The answer is C. x+2.



`( x^(4) +2 x^(3)-x-2 )/(x^(3) -1)`

Rearrange it:

`( x^(4) +2 x^(3)-x-2 )/(x^(3) -1)=( x^(4) -x+2 x^(3)-2 )/(x^(3) -1) =( x*x^(3) -x*1+2*x^(3)-2*1 )/(x^(3) -1)= (x( x^(3)-1)+2(x^(3)-1) )/(x^(3)-1) = \\ = ((x^(3)-1)(x+2))/(x^(3)-1)`

x³ - 1 can be cancelled out:

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