Arena Tutor - NBX Soluciones

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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. 📰 Alloy Collective 6021528 📰 Play Mini Golf 8162570 📰 Mind Blowing Grades In Manual Muscle Testing Heres How You Can Get There Fast 278035 📰 Zion National Park Vacation Rentals 350289 📰 Sapphire Preferred Benefits 3177380 📰 This Scandal Is Making Employees And Shoppers Lose Faith In The Companyare You Ready 7251431 📰 Tweed Suit 4703646 📰 Penske Jobs 8812708 📰 Flights To Punta Cana 7065338 📰 Pinayflix Just Made One Family Breakdown Into A Global Obsession 6315387 📰 When Can I Pull From My 401K 7346590 📰 Finally What Database Is Behind Every Appyoull Be Stunned By The Answer 5980886 📰 Given The Linear Equation S 3E 5 And We Need To Find E When S 20 Substitute S 20 Into The Equation 6152545 📰 Unlock Massive Returnscall Fidelity Investments 1 800 Xxx Number Now 922630 📰 Personal Hsa Account 319792