test","extracted_subject":"MATH","extracted_chapter":"QUADRATIC EQUATIONS","extracted_topic":"SOLUTION OF QUADRATIC INEQUATIONS AND MISCELLANEOUS EQUATIONS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2157.png?top_left_x=532&top_left_y=574&width=532&height=259&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab320ac0","slug":"the-remainder-obtained-when-the-polynomial-x-xsup3","content":"The remainder obtained when the polynomial\n\nx + x³ + x⁹ + x²⁷ + x⁸¹ + \\(x^{2^{243}}\\)is divided by x² –1 is:","options":[{"_id":"68a38a2e7f15af4716b87513","text":"6x + 1","sequence":0,"isCorrect":false},{"_id":"68a38a2e7f15af4716b87514","text":"5x + 1","sequence":1,"isCorrect":true},{"_id":"68a38a2e7f15af4716b87515","text":"4x","sequence":2,"isCorrect":false},{"_id":"68a38a2e7f15af4716b87516","text":"6x","sequence":3,"isCorrect":false}],"correct_answer":"5x + 1","explanation":"Put x² = 1 in the given polynomial\n\nx + x². x + (x²)⁴. x + (x²)¹³. x + (x²)⁴⁰. x + (x²)²⁴³\n\n= 5x + 1\n\n⇒ Choice (2) is correct.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.033Z","__v":0,"vector_store_id":"7ce4af16-53dd-48c2-ab5d-04a88120d187","updated_at":"2024-08-30T21:49:40.033Z","isStarred":false},"params":{"questionSlug":"the-remainder-obtained-when-the-polynomial-x-xsup3"}}]}]]

Question: The remainder obtained when the polynomial x + x<sup>3</sup> + x<sup>9</sup> + x<sup>27</sup> + x<s...

Solution