Answer:
The quotient of this division is  . The remainder here would be
. The remainder here would be  .
.
Step-by-step explanation:
The numerator  is a polynomial about
 is a polynomial about  with degree
 with degree  .
.
The divisor  is a polynomial, also about
 is a polynomial, also about  , but with degree
, but with degree  .
.
By the division algorithm, the quotient should be of degree  , while the remainder shall be of degree
, while the remainder shall be of degree  (i.e., the remainder would be a constant.) Let the quotient be
 (i.e., the remainder would be a constant.) Let the quotient be  with coefficients
 with coefficients  ,
,  , and
, and  .
.
 .
.
Start by finding the first coefficient of the quotient.
The degree-three term on the left-hand side is  . On the right-hand side, that would be
. On the right-hand side, that would be  . Hence
. Hence  .
.
Now, given that  , rewrite the right-hand side:
, rewrite the right-hand side:
 .
.
Hence:

Subtract  from both sides of the equation:
 from both sides of the equation:
 .
.
The term with a degree of two on the left-hand side has coefficient  . Since the only term on the right hand side with degree two would have coefficient
. Since the only term on the right hand side with degree two would have coefficient  ,
,  .
.
Again, rewrite the right-hand side:
 .
.
Subtract  from both sides of the equation:
 from both sides of the equation:
 .
.
By the same logic,  .
.
Hence the quotient would be  .
.