[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522618-105":59,"doc-detail-522618-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","descartes-rule-of-signs-worksheet-infinite-algebra-2","Descartes' Rule of Signs Worksheet - Infinite Algebra 2","","Describes a Descartes' Rule of Signs worksheet for Infinite Algebra 2. Students analyze a set of polynomial functions and determine the possible number of positive and negative real zeros for each function. Includes 20 problems requiring counts of positive and negative roots based on sign changes, plus a critical-thinking task asking for a polynomial with 0 possible positive real zeros and a specified set of possible negative real zeros, with examples provided.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/descartes-rule-of-signs-worksheet-infinite-algebra-2/522618/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/descartes-rule-of-signs-worksheet-infinite-algebra-2/522618.png","ImageObject",300,407,{"name":92,"@type":93},"River Wang","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the worksheet ask you to find for each polynomial?","Question",{"text":112,"@type":113},"It asks for the possible number of positive real zeros and the possible number of negative real zeros for each given polynomial function.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are problems 1–20 organized?",{"text":117,"@type":113},"Each problem presents a polynomial function and requires counting possible positive and negative zeros using Descartes' Rule of Signs.",{"name":119,"@type":110,"acceptedAnswer":120},"What is required in the critical thinking question (21)?",{"text":121,"@type":113},"Write a polynomial function that has 0 possible positive real zeros and 5, 3, or 1 possible negative real zero, and include one acceptable example.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522618,1791732645,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},1099514067438,"https://ap-avatar.wpscdn.com/avatar/100002539ee87300030?x-image-process=image/resize,m_fixed,w_180,h_180&k=1780474512215547542","Kuta Software-Infinite Algebra 2 Name___________________________________  \nDescartes' Rule of Signs Date________________ Period____  \nState the possible number of positive and negative zeros for each function.  \n1) f (x) = 3x4 + 20x2 − 32 2) f (x) = 5x4 − 42x2 + 49  \n3) f (x) = 4x3 − 12x2 − 5x + 1 4) f (x) = 2x4 − 3x3 + x  \n5) f (x) = 2x4 + 3x2 − 54 6) f (x) = x 6 − 64  \n7) f (x) = 9x6 − 3x5 + 33x4 − 11x3 + 18x2 − 6x 8) f (x) = 64x6 − 1  \n9) f (x) = 2x5 + 4x4 + 9x3 + 18x2 − 35x − 70  \n10) f (x) = 6x5 − 4x4 − 63x3 + 42x2 + 147x − 98  \n11) f (x) = 16x6 − 32x4 − 25x2 + 50 12) f (x) = x 7 − 64x  \n13) f (x) = x 6 − 64 14) f (x) = 8x6 + 9x3 + 1  \n15) f (x) = 27x6 + 26x3 − 1 16) f (x) = 27x9 − x 6 − 27x3 + 1  \n17) f (x) = 16x8 − 73x4 + 36 18) f (x) = 9x8 − 106x4 + 225  \n19) f (x) = x 6 − 64 20) f (x) = 16x8 − 153x4 + 81  \nCritical thinking questions:  \n21) Write a polynomial function that has 0 possible positive real zeros and 5, 3, or 1 possible negative real zero.  \nKuta Software-Infinite Algebra 2 Name___________________________________  \nDescartes' Rule of Signs Date________________ Period____  \nState the possible number of positive and negative zeros for each function.  \n1) f (x) = 3x4 + 20x2 − 32 2) f (x) = 5x4 − 42x2 + 49  \nPossible \\# positive real zeros: 1 Possible \\# positive real zeros: 2 or 0  \nPossible \\# negative real zeros: 1 Possible \\# negative real zeros: 2 or 0  \n3) f (x) = 4x3 − 12x2 − 5x + 1 4) f (x) = 2x4 − 3x3 + x  \nPossible \\# positive real zeros: 2 or 0 Possible \\# positive real zeros: 2 or 0  \nPossible \\# negative real zeros: 1 Possible \\# negative real zeros: 1  \n5) f (x) = 2x4 + 3x2 − 54 6) f (x) = x 6 − 64  \nPossible \\# positive real zeros: 1 Possible \\# positive real zeros: 1  \nPossible \\# negative real zeros: 1 Possible \\# negative real zeros: 1  \n7) f (x) = 9x6 − 3x5 + 33x4 − 11x3 + 18x2 − 6x 8) f (x) = 64x6 − 1  \nPossible \\# positive real zeros: 5, 3, or 1 Possible \\# positive real zeros: 1  \nPossible \\# negative real zeros: 0 Possible \\# negative real zeros: 1  \n9) f (x) = 2x5 + 4x4 + 9x3 + 18x2 − 35x − 70  \nPossible \\# positive real zeros: 1  \nPossible \\# negative real zeros: 4, 2, or 0  \n10) f (x) = 6x5 − 4x4 − 63x3 + 42x2 + 147x − 98  \nPossible \\# positive real zeros: 3 or 1  \nPossible \\# negative real zeros: 2 or 0  \n11) f (x) = 16x6 − 32x4 − 25x2 + 50 12) f (x) = x 7 − 64x  \nPossible \\# positive real zeros: 2 or 0 Possible \\# positive real zeros: 1  \nPossible \\# negative real zeros: 2 or 0 Possible \\# negative real zeros: 1  \n13) f (x) = x 6 − 64 14) f (x) = 8x6 + 9x3 + 1  \nPossible \\# positive real zeros: 1 Possible \\# positive real zeros: 0  \nPossible \\# negative real zeros: 1 Possible \\# negative real zeros: 2 or 0  \n15) f (x) = 27x6 + 26x3 − 1 16) f (x) = 27x9 − x 6 − 27x3 + 1  \nPossible \\# positive real zeros: 1 Possible \\# positive real zeros: 2 or 0  \nPossible \\# negative real zeros: 1 Possible \\# negative real zeros: 1  \n17) f (x) = 16x8 − 73x4 + 36 18) f (x) = 9x8 − 106x4 + 225  \nPossible \\# positive real zeros: 2 or 0 Possible \\# positive real zeros: 2 or 0  \nPossible \\# negative real zeros: 2 or 0 Possible \\# negative real zeros: 2 or 0  \n19) f (x) = x 6 − 64 20) f (x) = 16x8 − 153x4 + 81  \nPossible \\# positive real zeros: 1 Possible \\# positive real zeros: 2 or 0  \nPossible \\# negative real zeros: 1 Possible \\# negative real zeros: 2 or 0  \nCritical thinking questions:  \n21) Write a polynomial function that has 0 possible positive real zeros and 5, 3, or 1 possible negative real zero.  \nMany answers. Ex. f (x) = x 5 + x4 + x 3 + x 2 + x + 1  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiqaRaZU0g08A","https://ap.wps.com/l/cbCaiqaRaZU0g08A","pdf",34220,"English","# State the possible number of positive and negative zeros\n## Problems 1-20\n# Critical thinking question\n## Problem 21: construct a polynomial with specified zeros","[{\"question\":\"What does the worksheet ask you to find for each polynomial?\",\"answer\":\"It asks for the possible number of positive real zeros and the possible number of negative real zeros for each given polynomial function.\"},{\"question\":\"How are problems 1–20 organized?\",\"answer\":\"Each problem presents a polynomial function and requires counting possible positive and negative zeros using Descartes' Rule of Signs.\"},{\"question\":\"What is required in the critical thinking question (21)?\",\"answer\":\"Write a polynomial function that has 0 possible positive real zeros and 5, 3, or 1 possible negative real zero, and include one acceptable example.\"}]","Descartes' Rule of Signs Worksheet - Infinite Algebra 2 | PDF",1791425979]