Apply the Remainder Theorem to connect p(a), remainders, and factors x-a.
Use the Factor Theorem to decide whether x-a is a factor
Problem
Is \(x~-~2\) a factor of \(p(x)~=~x^3~-~8\)?
Big Picture
What this problem is really about
This is a factor test, and the Factor Theorem reduces it to one evaluation. The factor x minus 2 tells us to evaluate p at positive 2; if that value is zero, the division has no remainder and the factor condition holds. We’ll compute that value and use the zero test to decide.
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