Eric Nicholas K's answer to LockB's Secondary 3 A Maths Singapore question.

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Eric Nicholas K
Eric Nicholas K's answer
5997 answers (Tutor Details)
Q9 uses a very similar approach.

Also, the remainder will have a degree equal to at most 1 degree lower than the degree of the divisor, for your information. For example, in this case the divisor x2 - 1 has a degree of 2, so the degree of the remainder is at most 1 (most of the time, the degree of the remainder is exactly 1 lower than the degree of the divisor).