remainder theorem
an under-appreciated mathematical shortcut that allows us to find the remainder, given by p(a), when a polynomial p(x) is divided by (x – a) rather than tediously doing the long division to get the answer.
to find the remainder when p(x) = x¹⁰ – 13x² + 7x – 5 is divided by (x + 1), by remainder theorem, the remainder, p(–1), is (–1)¹⁰ – 13(–1)² + 7(–1) – 5 = –24—however, teachers often fail to remind students that the formula can’t be extrapolated to non-polynomials and non-linear factors.
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