Apply the Remainder Theorem to connect p(a), remainders, and factors x-a.
Use the Remainder Theorem to test possible rational roots
Problem
Use the Remainder Theorem to identify the roots of \(p(x)~=~x^3~-~6x^2~+~11x~-~6\) among \(1\), \(2\), and \(3\).
Big Picture
What this problem is really about
Each listed number is only a possible root until evaluation confirms it. We’ll substitute every candidate separately and keep precisely those for which p of a equals zero; by the Remainder Theorem, that zero value means division by x minus a leaves no remainder. Testing all three prevents us from stopping after the first successful candidate.
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