Comparison between multiplying and dividing polynomials

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

Steps for long division of polynomials:

Fills in missing terms in the divisor with zero coefficients

and insures the terms are sorted in decreasing order of exponents.

1) divides the leading terms

2) multiplies the quotient by the divisor

3) subtracts the partial product

4) brings down the next remainder

repeats the steps for each term

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steps for multiplication.

multiplies the first term in the first polynomial by the second polynomial;

multiplies the second term in the first polynomial by the second polynomial;

" 3rd term " " " " " " " ";

... etc etc etc.

SO how are they alike?

The are done term by term, featuring the multiplication of a monomial by a polynomial

How are they different?

Multiplication involves adding the exponents; Division involves subtracting the exponents;

What else?