[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-359080-105":59,"doc-detail-359080-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","factoring-expressions-using-the-gcf-b","Factoring Expressions Using the GCF (B)","","Factoring Expressions Using the GCF (B) provides directions to factor algebraic expressions completely using the Greatest Common Factor. It includes two-term expressions and mixed cases with two variables and three terms. The worksheet offers an answer key showing the extracted GCF and the resulting factored form for each problem, plus an error analysis challenge identifying and correcting a common factoring mistake.",{"@graph":69,"@context":123},[70,84,106],{"@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/factoring-expressions-using-the-gcf-b/359080/",{"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/factoring-expressions-using-the-gcf-b/359080.png","ImageObject",300,407,{"name":92,"@type":93},"Rhys","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-09-23",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What does the worksheet require you to do with each expression?","Question",{"text":113,"@type":114},"Factor each expression completely using the Greatest Common Factor (GCF).","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are the answers in the key presented?",{"text":118,"@type":114},"Each answer shows the factored form and lists the GCF with term-by-term division to justify it.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the student’s mistake in the error analysis challenge?",{"text":122,"@type":114},"The student divided 15a correctly but failed to divide 10b by the same GCF, so not every term was divided by the GCF.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},359080,1790241296,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":24,"preview_page_count":4},687207024643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Name:    \nFactoring Expressions Using the GCF ( B)  \nDirections: Factor each expression completely using the Greatest Common Factor (GCF) .  \nSection 1—Two-Term Expressions  \n1. 10x + 6 =   5. 25n − 15 =    \n2. 12n + 20 =   6. 27y − 18 =    \n3. 21y + 28 =   7. 40x − 16 =    \n4. 30x + 24 =    \nSection 2—Two Variables & Three Terms  \n8. 15x + 20y =   12. 8x + 12y + 4 =    \n9. 18a + 12b =   13. 15a + 10b + 5 =    \n10. 16n + 24m =   14. 9n + 15m − 6 =    \n11. 21x − 14y =    \n15. A student tried to factor the expression 15a + 10b as follows: Student’s work: 15a + 10b = 5(3a + 10b)  \nWhat is the student’s mistake?  \nCorrect answer:    \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)  \nANSWER KEY  \nSection 1:  \n1.) 10x + 6 → 2(5x + 3) (GCF=2; 10÷2=5, 6÷2=3)  \n2.) 12n + 20 → 4(3n + 5) (GCF=4; 12÷4=3, 20÷4=5)  \n3.) 21y + 28 → 7(3y + 4) (GCF=7; 21÷7=3, 28÷7=4)  \n4.) 30x + 24 → 6(5x + 4) (GCF=6; 30÷6=5, 24÷6=4)  \n5.) 25n − 15 → 5(5n − 3) (GCF=5; 25÷5=5, 15÷5=3)  \n6.) 27y − 18 → 9(3y − 2) (GCF=9; 27÷9=3, 18÷9=2)  \n7.) 40x − 16 → 8(5x − 2) (GCF=8; 40÷8=5, 16÷8=2)  \nSection 2:  \n8.) 15x + 20y → 5(3x + 4y) (GCF=5; 15÷5=3, 20÷5=4)  \n9.) 18a + 12b → 6(3a + 2b) (GCF=6; 18÷6=3, 12÷6=2)  \n10.) 16n + 24m → 8(2n + 3m) (GCF=8; 16÷8=2, 24÷8=3)  \n11.) 21x − 14y → 7(3x − 2y) (GCF=7; 21÷7=3, 14÷7=2)  \n12.) 8x + 12y + 4 → 4(2x + 3y + 1) (GCF=4; 8÷4=2, 12÷4=3, 4÷4=1)  \n13.) 15a + 10b + 5 → 5(3a + 2b + 1) (GCF=5; 15÷5=3, 10÷5=2, 5÷5=1)  \n14.) 9n + 15m − 6 → 3(3n + 5m − 2) (GCF=3; 9÷3=3, 15÷3=5, 6÷3=2)  \nError Analysis Challenge:  \nMistake: The student correctly divided 15a ÷ 5 = 3a but did not divide 10b by 5. Every term must be divided by the GCF: 10 ÷ 5 = 2, so 10b becomes 2b.  \nCorrect: 15a + 10b = 5(3a + 2b)  \nMashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)","cbCaivP62kykSmY4","https://ap.wps.com/l/cbCaivP62kykSmY4","pdf",644276,"English","# Section 1—Two-Term Expressions\n# Section 2—Two Variables & Three Terms\n# Error Analysis Challenge","[{\"question\":\"What does the worksheet require you to do with each expression?\",\"answer\":\"Factor each expression completely using the Greatest Common Factor (GCF).\"},{\"question\":\"How are the answers in the key presented?\",\"answer\":\"Each answer shows the factored form and lists the GCF with term-by-term division to justify it.\"},{\"question\":\"What is the student’s mistake in the error analysis challenge?\",\"answer\":\"The student divided 15a correctly but failed to divide 10b by the same GCF, so not every term was divided by the GCF.\"}]","Factoring Expressions Using the GCF (B) | PDF",1790136061]