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📰 Solution: Since $ p(x) $ is a cubic polynomial, when dividing by $ x^4 - 1 $, the remainder $ r(x) $ must be a polynomial of degree less than 4. However, because $ x^4 - 1 $ has roots $ \pm 1, \pm i $, and $ p(x) $ is real, the remainder can be expressed as any cubic or lower, but here we are to find the **actual remainder**, which is unique and of degree $ < 4 $. But since $ p(x) $ is already degree 3, and division by degree 4 polynomial yields a unique remainder of degree $ < 4 $, and since $ p(x) $ agrees with any degree ≤3 polynomial at these 4 points, we conclude: 📰 p(x) = \text{remainder of } p(x) \div (x^4 - 1) \quad \text{only if } \deg p < \deg(x^4 - 1) 📰 But $ p(x) $ is cubic, so remainder $ r(x) = p(x) $, but only if $ x^4 - 1 $ divides $ p(x) - r(x) $, which is not true unless $ p(x) $ is degree ≤3 — which it is. 📰 Pink Homecoming Dress 6085376 📰 The Shocking Rise Of Uvlack Behind The Scenes Of The Silent Outbreak 403194 📰 This Simple Yahoo Finance Sbux Hack Increasing High Yield Returns That Investors Ignore 5362401 📰 About Team Staff Contact Email Phone 3966507 📰 Riverside Plaza 6715743 📰 Oura Vs Whoop 5554044 📰 Learning Java These 7 Keywords Will Supercharge Your Coding Skills 547989 📰 Jennir 6443311 📰 How The Circuit Breaker Pattern Saves Apps From Failureheres How It Works 3824060 📰 This Badminton Racket Is So Powerful It Will Ruin Every Match Youve Ever Played 2952753 📰 The Secret List Of Bunny Names Most Owners Want To Hide But Cant 338143 📰 Undertale Character That Smokes 1982002 📰 Number Of Positions For The Non 25 Value 3 4193092 📰 Sourdough In Spanish 4539578 📰 Covidic 1501939