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
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;