[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522656-105":59,"doc-detail-522656-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","factors-and-zeros-infinite-algebra-2-worksheet","Factors and Zeros - Infinite Algebra 2 Worksheet","","This worksheet from Infinite Algebra 2 focuses on solving “factors and zeros” problems. It asks students to find all zeros of factored polynomial functions by listing the solutions. It also includes tasks to construct a polynomial function of least degree with integral coefficients given a set of zeros. Additional sections require factoring polynomials to determine all zeros, including cases that involve complex roots and multiplicities.",{"@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/factors-and-zeros-infinite-algebra-2-worksheet/522656/",{"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/factors-and-zeros-infinite-algebra-2-worksheet/522656.png","ImageObject",300,407,{"name":92,"@type":93},"Ophelia","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 I find all zeros for the factored functions in the worksheet?","Question",{"text":112,"@type":113},"Set each factor equal to zero and solve for x. List each solution as a zero of the polynomial, including any repeated roots.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What does “write a polynomial function of least degree with integral coefficients” mean here?",{"text":117,"@type":113},"Use the given zeros to form a polynomial from linear factors, then multiply them out. Choose the lowest-degree polynomial whose coefficients are integers.",{"name":119,"@type":110,"acceptedAnswer":120},"What should I do when the zeros include complex numbers or imaginary roots?",{"text":121,"@type":113},"Use the factors implied by the complex zeros. Complex roots typically come in conjugate pairs, so the resulting polynomial can still have real (often integer) coefficients.","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},522656,1791754077,{"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},7971461741311,"https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826","Kuta Software-Infinite Algebra 2 Name___________________________________  \nFactors and Zeros Date________________ Period____  \nFind all zeros.  \n1) f (x) = (2x − 1)(x − 5) 2) f (x) = (x − 3)(3x + 1)(x + 1)  \n3) f (x) = (2x + 1)(x + 1)(x − 1) 4) f (x) = x(5x − 2)(x2 + 1)  \n5) f (x) = x(x + 2)(x − 2)(3x2 − 4) 6) f (x) = (2x − 1)(x2 + 3)(2x2 − 5)  \n7) f (x) = x(2x − 1)(x − 1)(x + 1) 8) f (x) = (2x + 5)(x2 − 2x − 5)  \nWrite a polynomial function of least degree with integral coefficients that has the given zeros.  \n9) 3, 2, −2 10) 3, 1, −2, −4  \n11) 5, −1, 0 1  \n12) −3, −  3  , 5  \n13) 53~~ ~~ , 1, −1 14) 2, 53~~ ~~ , −5  \nFind all zeros by factoring each function.  \n15) f (x) = x 3 − 2x2 + x 16) f (x) = x 3 + 8  \n17) f (x) = x 4 − x 2 − 30 18) f (x) = x4 + x2 − 12  \n19) f (x) = x 6 − 64 20) f (x) = x 6 + 2x3 + 1  \nKuta Software-Infinite Algebra 2 Factors and Zeros  \nFind all zeros.  \n1) f (x) = (2x − 1)(x − 5)  \n{~~ ~~12~~ ~~ , 5 }  \nName___________________________________  \nDate________________ Period____  \n2) f (x) = (x − 3)(3x + 1)(x + 1)  \n{3, − ~~ ~~13~~ ~~ , −1 }  \n3) f (x) = (2x + 1)(x + 1)(x − 1) 4) f (x) = x(5x − 2)(x2 + 1)  \n{− ~~ ~~12~~ ~~ , −1, 1 } {0, ~~ ~~25~~ ~~ , i, −i}  \n5) f (x) = x(x + 2)(x − 2)(3x2 − 4) 6) f (x) = (2x − 1)(x2 + 3)(2x2 − 5)  \n0, −2, 2, 2 3 3 , − 2 3 3 } { 12 , i 3 , −i 3 , 102 , − 102 }  \n{ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~  \n7) f (x) = x(2x − 1)(x − 1)(x + 1) 8) f (x) = (2x + 5)(x2 − 2x − 5)  \n0, ~~ ~~12~~ ~~ , 1, −1 } {− ~~ ~~52~~ ~~ , 1 + 6 , 1 − 6 }  \n{  \nWrite a polynomial function of least degree with integral coefficients that has the given zeros.  \n9) 3, 2, −2 10) 3, 1, −2, −4  \nf (x) = x 3 − 3x2 − 4x + 12 f (x) = x4 + 2x3 − 13x2 − 14x + 24  \n11) 5, −1, 0 1  \n12) −3, − ~~ ~~ , 5  \nf (x) = x 3 − 4x2 − 5x 3  \nf (x) = 3x3 − 5x2 − 47x − 15  \n5   5  \n13) , 1, −1 14) 2, , −5  \n3 3  \nf (x) = 3x3 − 5x2 − 3x + 5 f (x) = 3x3 + 4x2 − 45x + 50  \nFind all zeros by factoring each function.  \n15) f (x) = x 3 − 2x2 + x 16) f (x) = x 3 + 8  \n{0, 1 mult. 2} {−2, 1 + i 3 , 1 − i 3 }  \n17) f (x) = x 4 − x 2 − 30 18) f (x) = x4 + x2 − 12  \n{ 6 , − 6 , i 5 , −i 5 } {2i, −2i, 3 , − 3 }  \n19) f (x) = x 6 − 64 20) f (x) = x 6 + 2x3 + 1  \n{−2, 1 + i 3 , 1 − i 3 , 2, −1 + i 3 , −1 − i 3 } {−1 mult. 2, ~~ ~~1~~ ~~+~~ ~~i2~~ ~~3~~ ~~ mult. 2, ~~ ~~1~~ ~~−~~ ~~i2~~ ~~3~~ ~~ mult. 2 }  \nCreate your own worksheets like this one with Infinite Algebra 2. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaisVJwlCtj0AV","https://ap.wps.com/l/cbCaisVJwlCtj0AV","pdf",35583,"English","# Find all zeros\n## Given factored functions (1–8)\n# Write a polynomial of least degree\n## Given zeros (9–14)\n# Find all zeros by factoring\n## Polynomial functions (15–20)","[{\"question\":\"How do I find all zeros for the factored functions in the worksheet?\",\"answer\":\"Set each factor equal to zero and solve for x. List each solution as a zero of the polynomial, including any repeated roots.\"},{\"question\":\"What does “write a polynomial function of least degree with integral coefficients” mean here?\",\"answer\":\"Use the given zeros to form a polynomial from linear factors, then multiply them out. Choose the lowest-degree polynomial whose coefficients are integers.\"},{\"question\":\"What should I do when the zeros include complex numbers or imaginary roots?\",\"answer\":\"Use the factors implied by the complex zeros. Complex roots typically come in conjugate pairs, so the resulting polynomial can still have real (often integer) coefficients.\"}]","Factors and Zeros - Infinite Algebra 2 Worksheet | PDF",1791426025]