Respuesta :
The quotient is [tex]\rm x^2+x+1[/tex].
Given
The given equation is;
[tex]\rm \dfrac{x^3+1}{x-1}[/tex]
What is synthetic division?
The synthetic division method is the shortcut method to divide polynomials.
It is also known as the polynomial division method of a special case when it is divided by the linear factor.
Therefore,
The quotient is;
[tex]\rm =\dfrac{x^3+1}{x-1}\\\\ = \dfrac{x^3+x^2+x-x^2-x-1}{x-1}\\\\ =\dfrac{x(x^2+x+1) - 1((x^2+x+1) }{x-1}\\\\\rm = \dfrac{(x-1) (x^2+x+1)}{x-1}\\\\ = x^2+x+1[/tex]
Hence, the quotient is [tex]\rm x^2+x+1[/tex].
To know more about Synthetic division click the link given below.
https://brainly.com/question/25997349
Answer:
its not B on edge but I think its A
Step-by-step explanation:
I put B and got it wrong just took the test lol
