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If the quotient of a certain binomial and 20x2 is is the polynomial
You use long division of polynomials.
You multiply each term of one binomial by each term of the other binomial. In fact, this works for multiplying any polynomials: multiply each term of one polynomial by each term of the other one. Then add all the terms together.
monomials are just polynomials with one term, i.e. 2xy2, n3, etc. A binomial has two terms, i.e. 3xy2+2, etc.
Add together the coefficients of "like" terms. Like terms are those that have the same powers of the variables in the polynomials.