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The remainder theorem says dividing P(x) by (x − a) leaves remainder P(a). Synthetic division produces both the quotient and that remainder in a single pass.
Remainder theorem
P(x) = (x − a)·Q(x) + P(a)
P(2) = 16 − 12 + 5 = 9, so the remainder is 9 and the quotient is 2x² + x + 2.
Write it as (x − (−a)) and evaluate at −a instead.