Which of the following expressions is this one equivalent to? ( {x}^(4)+ 2 {x}^(3) - x - 2) / ( {x}^(3) - 1) ___________________________________________ ○A. {x}^(2) + x + 1 ○B. …

Question

Which of the following expressions is this one equivalent to?


`( {x}^(4)+ 2 {x}^(3) - x - 2) / ( {x}^(3) - 1)`
___________________________________________
○A.

`{x}^(2) + x + 1`
○B.

`{x}^(2) + 3x + 2`
○C.

`x + 2`
○D.

`2x - 5 - \frac{3}{ {x}^(3) - 1 }`​

Answer 1

C. x+2

Explanation:

The given expressions are two polynomials which have to be divided in order to find the quotient. The long division method will be used to find the quotient of the two terms.

The long division is done and the picture is attached for detail.

From the picture, we can see that the correct answer is:

C. x+2 ..

Answer 2

○C. x + 2

Explanation:

x^4 + 2x^3 -x-2

-------------------------

x^3 -1

Factor the numerator by grouping. Take an x^3 from the first 2 terms and -1 from the last 2 terms

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

-------------------------

x^3 -1

now lets factor out the x+2

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

-------------------------

x^3 -1

Canceling out the x^3-1, we are left with

x+2