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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. 📰 Bg3 Subclasses Unlocked The Hidden System Youve Been Ignoring 9595171 📰 The Unseen Force Of Tamilgun That Changed Wars Cultures And Fates 5723010 📰 Women Chase Jacksonville Provides Craigslist Florida Listings That Shanghai Smokers Dont Want You To See 1036830 📰 How A Single Action Triggers The Powerful Domino Effect You Cant Ignore 1733541 📰 The Mysterious Power Of 40 Seconds You Wont Forget 4888523 📰 Purduesports Football 1132650 📰 Echoes Of The Past In 22180 Why This Vienna Street Holds The Key To A Shocking Conspiracy 1149447 📰 Your Pokemon Trade Secrets The Ultimate Price Checker Youll Need Today 2961307 📰 Stop Trading Blind How Full Service Stock Brokers Boost Your Performance Like A Pro 2248469 📰 Settingd Exposed The Motivation Hack Every Successful Visionary Uses Now 5917788 📰 Biggest Stock Losers Todayinvestors Are Losing Thousands Overnight What You Need To Know Now 2266326 📰 Unreal Game Engine 4322480 📰 Struggling With Journal Software Microsofts Latest Update Solves It Allclick To Learn 8198108 📰 Download Windows 11 Assistant 8583930 📰 Grand Bear Resort 2919333