Apply the Remainder Theorem to connect p(a), remainders, and factors x-a.
Use the Remainder Theorem to find a remainder from a divisor x-a
Problem
Use the Remainder Theorem to find the remainder when \(p(x)~=~x^3~-~2x~+~5\) is divided by \(x~-~2\).
Big Picture
What this problem is really about
The divisor already has the form x minus a, so the Remainder Theorem turns division into one polynomial evaluation. We’ll identify a as positive 2, substitute that value into every x term of p, and simplify. The resulting function value is the remainder, with no need to compute the quotient.
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