Apply the Remainder Theorem to connect p(a), remainders, and factors x-a.
Evaluate a polynomial at a given value to find the remainder
Problem
For \(p(x)~=~x^3~-~2x~+~5\), evaluate \(p(2)\) to find the remainder.
Big Picture
What this problem is really about
Finding the remainder here is the same as evaluating the polynomial at the given input. We’ll replace every x by 2, evaluate each term with its original sign, and add those term values. Keeping the linear term as negative 2 times 2 is the key to preserving the polynomial’s value.
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