Answer
Similarity: each term of the polynomial is divided by the monomial term
Difference: operations needed to carry out the process
Preferred: multiplication by the reciprocal
Work Step by Step
Multiplying by the reciprocal of the monomial will result to the Distributive Property where each term of the polynomial will be divided by the monomial. This is also the result when long division is performed (i.e. each term of the polynomial is divided by the monomial).
The difference between the two is the set of operations needed in the solution. Multiplying by the reciprocal involves multiplication and division. The long division method, however, uses division, multiplication, and subtraction.
Between the two processes, I prefer the multiplication by the reciprocal more since this method gives the result in a quicker manner.
