] gives the quotient of p and q, treated as polynomials in x, with any remainder dropped.
See the Mathematica book: Section 3.3.4.
See also: PolynomialRemainder, PolynomialReduce, PolynomialGCD, Apart, Cancel, Quotient.
This gives the quotient and remainder upon dividing the first polynomial by the second one, both separately and then together.
In this example the degree of the remainder is zero, which must be the case because the divisor is of degree one.
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