[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-522717-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-522717-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","more-on-factors-zeros-and-dividing","More on Factors, Zeros, and Dividing","","Worksheet exercises for Infinite Algebra 2 focused on factoring polynomial expressions and determining all zeros. Each problem gives a function f(x) and one known factor or a known zero, then asks students to factor the polynomial completely and list the zeros, including multiplicities when applicable. Problems cover different degrees (cubic and quartic) and practice combining algebraic structure with sign and root identification.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/more-on-factors-zeros-and-dividing/522717/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/more-on-factors-zeros-and-dividing/522717.png","ImageObject",300,407,{"name":42,"@type":43},"Jacob","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",10,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What do the problems ask you to do with each function f(x)?","Question",{"text":63,"@type":64},"Factor the polynomial completely and find all zeros of f(x).","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How is the given information used in each problem?",{"text":68,"@type":64},"Each item provides either one factor or one zero, guiding the factoring and zero-finding process.",{"name":70,"@type":61,"acceptedAnswer":71},"Do the worksheet problems include multiplicities for zeros?",{"text":72,"@type":64},"Yes. Some answers specify repeated zeros (for example, a zero with a given multiplicity).","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522717,1791490642,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":55,"slug":125},"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":33,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":55,"preview_page_count":4},962084931830,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Kuta Software-Infinite Algebra 2 Name___________________________________  \nMore on Factors, Zeros, and Dividing Date________________ Period____  \nFactor each and find all zeros. One factor has been given.  \n1) f (x) = x 3 + 9x2 + 23x + 15; x + 5 2) f (x) = x 3 − x 2 − 14x + 24; x − 3  \n3) f (x) = x 4 + 3x3 − 13x2 − 15x; x − 3 4) f (x) = x 3 − 12x2 + 47x − 60; x − 3  \n5) f (x) = x 3 − 7x2 + 2x + 40; x − 5 6) f (x) = x 3 − 3x2 − 9x + 27; x − 3  \n7) f (x) = 10x3 + 37x2 + 37x + 6; 5x + 1 8) f (x) = 25x3 + 150x2 + 131x + 30; 5x + 3  \n9) f (x) = 5x3 + 21x2 − 21x − 5; x + 5 10) f (x) = 3x3 − 4x2 − 9x + 10; x − 2  \n11) f (x) = 5x3 + 9x2 − 26x − 24; x + 3 12) f (x) = 6x3 + 7x2 − 1; 2x + 1  \nFactor each and find all zeros. One zero has been given.  \n13) f (x) = 5x3 + 4x2 − 20x − 16; 2 14) f (x) = 25x4 − 40x3 − 19x2 − 2x; − ~~ ~~15  \n15) f (x) = 3x4 + 5x3 + 81x + 135; − ~~ ~~53~~ ~~ 16) f (x) = 2x4 − x 3 − 18x2 + 9x; −3  \n3 2 5 18) f (x) = 3x3 + 4x2 − 35x − 12; 3  \n17) f (x) = 10x − 41x + 32x + 20; 2  \nKuta Software-Infinite Algebra 2 Name   \nMore on Factors, Zeros, and Dividing Date  Period   \nFactor each and find all zeros. One factor has been given.  \n1) f (x) = x 3 + 9x2 + 23x + 15; x + 5  \nFactors to: f (x) = (x + 1)(x + 3)(x + 5)  \nZeros: {−1, −3, −5}  \n3) f (x) = x 4 + 3x3 − 13x2 − 15x; x − 3  \nFactors to: f (x) = x(x + 1)(x + 5)(x − 3)  \nZeros: {0, −1, −5, 3}  \n5) f (x) = x 3 − 7x2 + 2x + 40; x − 5  \nFactors to: f (x) = (x + 2)(x − 4)(x − 5)  \nZeros: {−2, 4, 5}  \n7) f (x) = 10x3 + 37x2 + 37x + 6; 5x + 1  \nFactors to: f (x) = (2x + 3)(x + 2)(5x + 1)  \nZeros: {− ~~ ~~32~~ ~~ , −2, − ~~ ~~15~~ ~~ }  \n9) f (x) = 5x3 + 21x2 − 21x − 5; x + 5  \nFactors to: f (x) = (5x + 1)(x − 1)(x + 5)  \nZeros: {− ~~ ~~15~~ ~~ , 1, −5 }  \n2) f (x) = x 3 − x 2 − 14x + 24; x − 3  \nFactors to: f (x) = (x − 2)(x + 4)(x − 3)  \nZeros: {2, −4, 3}  \n4) f (x) = x 3 − 12x2 + 47x − 60; x − 3  \nFactors to: f (x) = (x − 4)(x − 5)(x − 3)  \nZeros: {4, 5, 3}  \n6) f (x) = x 3 − 3x2 − 9x + 27; x − 3  \nFactors to: f (x) = (x + 3)(x − 3)2  \nZeros: {−3, 3 mult. 2}  \n8) f (x) = 25x3 + 150x2 + 131x + 30; 5x + 3  \nFactors to: f (x) = (5x + 2)(x + 5)(5x + 3)  \nZeros: {− ~~ ~~25~~ ~~ , −5, − ~~ ~~35~~ ~~ }  \n10) f (x) = 3x3 − 4x2 − 9x + 10; x − 2  \nFactors to: f (x) = (3x + 5)(x − 1)(x − 2)  \nZeros: {− ~~ ~~53~~ ~~ , 1, 2 }  \n11) f (x) = 5x3 + 9x2 − 26x − 24; x + 3  \nFactors to: f (x) = (5x + 4)(x − 2)(x + 3)  \nZeros: {− ~~ ~~45~~ ~~ , 2, −3 }  \n12) f (x) = 6x3 + 7x2 − 1; 2x + 1  \nFactors to: f (x) = (3x − 1)(x + 1)(2x + 1)  \nZeros: {~~ ~~13~~ ~~ , −1, − ~~ ~~12~~ ~~ }  \nFactor each and find all zeros. One zero has been given.  \n13) f (x) = 5x3 + 4x2 − 20x − 16; 2  \nFactors to: f (x) = (5x + 4)(x + 2)(x − 2)  \nZeros: {− ~~ ~~45~~ ~~ , −2, 2 }  \n4 3 5  \n15) f (x) = 3x + 5x + 81x + 135; −  3  \nFactors to: f (x) = (x + 3)(x2 − 3x + 9)(3x + 5)  \nZeros: {−3, ~~ ~~3~~ ~~+~~ ~~3i2~~ ~~3~~ ~~ , ~~ ~~3~~ ~~−~~ ~~3i2~~ ~~3~~ ~~ , − ~~ ~~53~~ ~~ }  \n17) f (x) = 10x3 − 41x2 + 32x + 20; 52  \nFactors to: f (x) = (5x + 2)(x − 2)(2x − 5)  \nZeros: {− ~~ ~~25~~ ~~ , 2, ~~ ~~52~~ ~~ }  \n4 3 2 1  \n14) f (x) = 25x − 40x − 19x − 2x; −  5  \nFactors to: f (x) = x(5x + 1)2 (x − 2)  \nZeros: {0, − ~~ ~~15 mult. 2, 2}  \n16) f (x) = 2x4 − x 3 − 18x2 + 9x; −3  \nFactors to: f (x) = x(2x − 1)(x − 3)(x + 3)  \nZeros: {0, 12~~ ~~ , 3, −3 }  \n18) f (x) = 3x3 + 4x2 − 35x − 12; 3  \nFactors to: f (x) = (3x + 1)(x + 4)(x − 3)  \nZeros: {− ~~ ~~13~~ ~~ , −4, 3 }  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaieHfInyfNRMC","https://ap.wps.com/l/cbCaieHfInyfNRMC","pdf",36777,"English","# Factor each and find all zeros\n## One factor has been given\n## One zero has been given","[{\"question\":\"What do the problems ask you to do with each function f(x)?\",\"answer\":\"Factor the polynomial completely and find all zeros of f(x).\"},{\"question\":\"How is the given information used in each problem?\",\"answer\":\"Each item provides either one factor or one zero, guiding the factoring and zero-finding process.\"},{\"question\":\"Do the worksheet problems include multiplicities for zeros?\",\"answer\":\"Yes. Some answers specify repeated zeros (for example, a zero with a given multiplicity).\"}]","More on Factors, Zeros, and Dividing | PDF",1791426091]