[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-265100-105":59,"doc-detail-265100-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","solving-quadratic-equations-by-factoring-quick-review-and-helpful-hints","Solving Quadratic Equations by Factoring - Quick Review and Helpful Hints","","Solving quadratic equations by factoring focuses on converting a quadratic to factored form and applying the zero-product property. The materials guide students to set the product equal to 0, then solve by setting each factor equal to 0 to find the solution values. Worked examples and word problems connect factoring to roots, x-intercepts, and model-based zeros from area and projectile-height contexts. Answer keys provide step-by-step reasoning for multiple practice items.",{"@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/solving-quadratic-equations-by-factoring-quick-review-and-helpful-hints/265100/",{"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/solving-quadratic-equations-by-factoring-quick-review-and-helpful-hints/265100.png","ImageObject",300,407,{"name":92,"@type":93},"Ben ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-21","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the main method for solving quadratic equations by factoring?","Question",{"text":113,"@type":114},"Factor the quadratic, set the factored expression equal to 0, and use the zero-product property. Then solve by setting each factor equal to 0.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the zero-product property help when you factor a quadratic?",{"text":118,"@type":114},"If (x − p)(x − q) = 0, then at least one factor must be 0. Solving each factor equal to 0 gives the possible values of x.",{"name":120,"@type":111,"acceptedAnswer":121},"How are roots related to graphing in these problems?",{"text":122,"@type":114},"Roots are where the curve meets the x-axis. For factored forms, the roots correspond to the x-values that make the quadratic equal to zero.","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},265100,1789392391,{"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":81,"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":130,"read_time":39},2336478951081,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Practice 􀀏 Progress 􀀏 Succeed | GED Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nSolving Quadratic Equations by Factoring  \n\n| Name:   | D | ate:   | S | core:   / 18 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nSet the equation equal to 0, factor the quadratic, then use the zero-product property: if a product is 0, at least one factor is 0. So if (x 􀀀 p)(x 􀀀 q) = 0, then x = p or x = q.  \n▷ Example: Solve x2 + 5x + 6 = 0 . Work: Factor: (x + 2)(x + 3) = 0 . Set each factor to 0: x + 2 = 0 or x + 3 = 0 . ⋆ Answer: x = 􀀀2 or x = 􀀀3  \nRoots: where the curve meets the x-axis.  \n♦ Word Problems  \n15. A square sign has area 4 square feet. If side length is represented by x, solve x2 􀀀 4 = 0 for the possible mathematical values of x.  \n16. A projectile-height model has zeros found by solving x2 + 9x + 20 = 0 . Solve for the two zero values.  \n17. A rectangular area model becomes zero at the boundary values of x2 􀀀 6x + 8 = 0 . Solve for those values.  \n18. If (x 􀀀 3)(x + 5) = 0, 􀀂nd all values of x.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | GED Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \nStep-by-Step Explanations  \n1. Start by naming the process: Factor the quadratic, then use the zeroproduct property by setting each factor equal to zero. The setup/work is (x + 2)(x + 3) = 0, so x = 􀀀2 or 􀀀3 . So the 􀀂nal answer is x = 􀀀2, 􀀀3 .  \n2. A good way to think about this is: Factor the quadratic, then use the zeroproduct property by setting each factor equal to zero. The setup/work is (x 􀀀 3)(x 􀀀 4) = 0, so x = 3 or 4. So the 􀀂nal answer is x = 3 , 4.  \n3. Step by step: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is (x + 3)(x 􀀀 2) = 0, sox = 2 or 􀀀3 . So the 􀀂nal answer is x = 2 , 􀀀3 .  \n4. Take it one move at a time: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is (x􀀀3)(x+3) = 0, so x = 3 or 􀀀3 . So the 􀀂nal answer is x = 3 , 􀀀3 .  \n5. Start by naming the process: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is x(x 􀀀 5) = 0 , so x = 0 or 5. So the 􀀂nal answer is x = 0 , 5.  \n6. A good way to think about this is: Factor the quadratic, then use the zeroproduct property by setting each factor equal to zero. The setup/work is (x + 4)(x 􀀀 2) = 0, so x = 2 or 􀀀4 . So the 􀀂nal answer is x = 2 , 􀀀4 .  \n7. Step by step: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is (x 􀀀 2)2 = 0, so x = 2 (one repeated root) . So the 􀀂nal answer is x = 2 .  \n8. Take it one move at a time: Factor the quadratic, then use the zero-product property by setting each factor equal to zero. The setup/work is","cbCaivERT4RdMJUq","https://ap.wps.com/l/cbCaivERT4RdMJUq","pdf",111663,"English","# Quick Review and Helpful Hints\n## Zero-product property\n## Roots and x-intercepts\n## Word Problems\n## Answer Keys - Step-by-Step Explanations","[{\"question\":\"What is the main method for solving quadratic equations by factoring?\",\"answer\":\"Factor the quadratic, set the factored expression equal to 0, and use the zero-product property. Then solve by setting each factor equal to 0.\"},{\"question\":\"How does the zero-product property help when you factor a quadratic?\",\"answer\":\"If (x − p)(x − q) = 0, then at least one factor must be 0. Solving each factor equal to 0 gives the possible values of x.\"},{\"question\":\"How are roots related to graphing in these problems?\",\"answer\":\"Roots are where the curve meets the x-axis. For factored forms, the roots correspond to the x-values that make the quadratic equal to zero.\"}]","Solving Quadratic Equations by Factoring - Quick Review and Helpful Hints | PDF"]