Question

In what ways are the steps for the long division of polynomials algorithm similar to the steps for the multiplying polynomials algorithm? In what ways are they different?

Answer 1

Undermentioned explanation, similarity & dissimilarity between long division & multiplication of polynomials

Explanation:

Long Division of Polynomial steps :

Complete missing terms in divisor with zero coefficients, sort terms in decreasing exponential order

Divide leading term, multiply divisor x quotient, subtract partial product & carry down remainder ............ (continue same)

Multiplication of Polynomial steps :

Multiply the 1st, 2nd, 3rd term(s) in the first polynomial with 1st, 2nd, 3rd consecutive term(s) in the second polynomial........... (go on)

Similarity (ies) : Both involve term by term treatment, multiplying monomial & polynomial

Dissimilarity (ies) : Division includes subtracting of exponential power. However, multiplication includes adding of exponential power