College Algebra / Unit 7 Alg 368 short lesson, about 20 seconds
The Remainder Theorem
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The idea
The Remainder Theorem states that dividing a polynomial f(x) by x − k leaves the remainder f(k).
In practice
For f(x) = x³ − 3x + 2 divided by x − 2: f(2) = 8 − 6 + 2 = 4, so the remainder is 4 before any division runs — evaluation and division, one number.
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