[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522788-105":59,"doc-detail-522788-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","the-remainder-theorem-evaluate-functions-and-divide-polynomials","The Remainder Theorem - Evaluate Functions and Divide Polynomials","","Worksheets for Infinite Algebra 2 on the Remainder Theorem. Students evaluate multiple polynomial functions at given values and determine whether specified binomials are factors of the corresponding polynomials, recording Yes/No responses. The sheet also includes polynomial division problems, requiring simplified quotient and remainder forms (R ...). Designed for practice consolidating theorem-based evaluation, factor checks, and long-division style outcomes across varied variables and degrees.",{"@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/the-remainder-theorem-evaluate-functions-and-divide-polynomials/522788/",{"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/the-remainder-theorem-evaluate-functions-and-divide-polynomials/522788.png","ImageObject",300,407,{"name":92,"@type":93},"Maya Linwood","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you use the Remainder Theorem to evaluate a polynomial at a specific value?","Question",{"text":112,"@type":113},"Substitute the given value into the polynomial. The result gives the remainder associated with that input under the Remainder Theorem setup.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does it mean to check whether a binomial is a factor of a polynomial?",{"text":117,"@type":113},"A binomial (like (x+a)) is a factor exactly when the corresponding remainder is 0 after evaluating using the theorem.",{"name":119,"@type":110,"acceptedAnswer":120},"What output is expected for the “Divide” problems?",{"text":121,"@type":113},"Each division result should be expressed as a quotient in simplified form together with a remainder written as R followed by the remainder value.","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},522788,1791496830,{"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":44,"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},962084928432,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Kuta Software-Infinite Algebra 2 Name___________________________________  \nThe Remainder Theorem Date________________ Period____  \nEvaluate each function at the given value.  \n1) f (x) = −x3 + 6x − 7 at x = 2 2) f (x) = x 3 + x 2 − 5x − 6 at x = 2  \n3) f (a) = a 3 + 3a2 + 2a + 8 at a = −3 4) f (a) = a 3 + 5a2 + 10a + 12 at a = −2  \n5) f (a) = a4 + 3a3 − 17a2 + 2a − 7 at a = 3 6) f (x) = x 5 − 47x3 − 16x2 + 8x + 52 at x = 7  \nState if the given binomial is a factor of the given polynomial.  \n7) (k3 − k2 − k − 2) ÷ (k − 2) 8) (b4 − 8b3 − b2 + 62b − 34) ÷ (b − 7)  \n9) (n4 + 9n3 + 14n2 + 50n + 9) ÷ (n + 8) 10) ( p4 + 6 p3 + 11 p2 + 29 p − 13) ÷ ( p + 5)  \n11) ( p4 − 8 p3 + 10 p2 + 2 p + 4) ÷ ( p − 2) 12) (n5 − 25n3 − 7n2 − 37n − 18) ÷ (n + 5)  \n13) (x5 + 6x4 − 3x2 − 22x − 29) ÷ (x + 6) 14) (n4 + 10n3 + 21n2 + 6n − 8) ÷ (n + 2)  \nDivide.  \n15) ( p4 + 5 p3 − 11 p2 − 25 p + 29) ÷ ( p + 6) 16) (8k3 − 66k2 + 14k + 8) ÷ (k − 8)  \n17) (x4 + 11x3 + 33x2 + 24x + 32) ÷ (x + 6) 18) (6v3 + 42v2 − 50v − 20) ÷ (v + 8)  \n19) (6b4 + 53b3 + 32b2 − 61b + 19) ÷ (b + 8) 20) (4n3 − 9n2 + 9n + 3) ÷ (n − 1)  \n21) (6a3 + 20a2 − 15a + 9) ÷ (a + 4) 22) (n4 − 6n3 − 10n2 + 20n + 15) ÷ (n + 2)  \n23) ( p5 + 8 p4 + 2 p2 + 19 p + 16) ÷ ( p + 8) 24) (x4 − 2x3 − 16x2 + 28x + 9) ÷ (x − 4)  \n25) (r5 + 6r4 − 13r3 − 5r2 − 8r + 14) ÷ (r − 2) 26) (8v5 + 32v4 + 5v + 20) ÷ (v + 4)  \nKuta Software-Infinite Algebra 2  \nThe Remainder Theorem  \nEvaluate each function at the given value.  \n1) f (x) = −x3 + 6x − 7 at x = 2  \n−3  \nName___________________________________  \nDate________________ Period____  \n2) f (x) = x 3 + x 2 − 5x − 6 at x = 2  \n−4  \n3) f (a) = a 3 + 3a2 + 2a + 8 at a = −3 4) f (a) = a 3 + 5a2 + 10a + 12 at a = −2 2 4  \n5) f (a) = a4 + 3a3 − 17a2 + 2a − 7 at a = 3 6) f (x) = x 5 − 47x3 − 16x2 + 8x + 52 at x = 7 8 10  \nState if the given binomial is a factor of the given polynomial.  \n7) (k3 − k2 − k − 2) ÷ (k − 2) 8) (b4 − 8b3 − b2 + 62b − 34) ÷ (b − 7)  \nYes No  \n9) (n4 + 9n3 + 14n2 + 50n + 9) ÷ (n + 8) 10) ( p4 + 6 p3 + 11 p2 + 29 p − 13) ÷ ( p + 5)  \nNo No  \n11) ( p4 − 8 p3 + 10 p2 + 2 p + 4) ÷ ( p − 2) 12) (n5 − 25n3 − 7n2 − 37n − 18) ÷ (n + 5)  \nYes No  \n13) (x5 + 6x4 − 3x2 − 22x − 29) ÷ (x + 6) 14) (n4 + 10n3 + 21n2 + 6n − 8) ÷ (n + 2)  \nNo Yes  \nDivide.  \n15) ( p4 + 5 p3 − 11 p2 − 25 p + 29) ÷ ( p + 6) 16) (8k3 − 66k2 + 14k + 8) ÷ (k − 8)  \np 3 − p2 − 5 p + 5, R −1 8k2 − 2k − 2, R −8  \n17) (x4 + 11x3 + 33x2 + 24x + 32) ÷ (x + 6) 18) (6v3 + 42v2 − 50v − 20) ÷ (v + 8)  \nx 3 + 5x2 + 3x + 6, R −4 6v2 − 6v − 2, R −4  \n19) (6b4 + 53b3 + 32b2 − 61b + 19) ÷ (b + 8) 20) (4n3 − 9n2 + 9n + 3) ÷ (n − 1)  \n6b3 + 5b2 − 8b + 3, R −5 4n2 − 5n + 4, R 7  \n21) (6a3 + 20a2 − 15a + 9) ÷ (a + 4) 22) (n4 − 6n3 − 10n2 + 20n + 15) ÷ (n + 2)  \n6a2 − 4a + 1, R 5 n 3 − 8n2 + 6n + 8, R −1  \n23) ( p5 + 8 p4 + 2 p2 + 19 p + 16) ÷ ( p + 8) 24) (x4 − 2x3 − 16x2 + 28x + 9) ÷ (x − 4)  \np4 + 2 p + 3, R −8 x 3 + 2x2 − 8x − 4, R −7  \n25) (r5 + 6r4 − 13r3 − 5r2 − 8r + 14) ÷ (r − 2) 26) (8v5 + 32v4 + 5v + 20) ÷ (v + 4)  \nr4 + 8r3 + 3r2 + r − 6, R 2 8v4 + 5  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaio45cjwCSeos","https://ap.wps.com/l/cbCaio45cjwCSeos","pdf",37799,"English","# Evaluate each function at the given value\n# State if the given binomial is a factor of the given polynomial\n# Divide","[{\"question\":\"How do you use the Remainder Theorem to evaluate a polynomial at a specific value?\",\"answer\":\"Substitute the given value into the polynomial. The result gives the remainder associated with that input under the Remainder Theorem setup.\"},{\"question\":\"What does it mean to check whether a binomial is a factor of a polynomial?\",\"answer\":\"A binomial (like (x+a)) is a factor exactly when the corresponding remainder is 0 after evaluating using the theorem.\"},{\"question\":\"What output is expected for the “Divide” problems?\",\"answer\":\"Each division result should be expressed as a quotient in simplified form together with a remainder written as R followed by the remainder value.\"}]","The Remainder Theorem - Evaluate Functions and Divide Polynomials | PDF",1791426172]