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FilledSmallSquarePolynomialQuotient[p, q, x] gives the quotient of p and q, treated as polynomials in x, with any remainder dropped.

FilledSmallSquare See The Mathematica Book: Section 3.3.4.

FilledSmallSquare See also: PolynomialRemainder, PolynomialReduce, PolynomialGCD, Apart, Cancel, Quotient.

Further Examples