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The document presents 16 distinct algebra problems, followed by a comprehensive answer key that details the step-by-step factorisation process and the final roots for each equation. Designed for supplemental math instruction, the material helps learners build proficiency in solving quadratic equations with integer coefficients and constants, reinforcing algebraic manipulation skills through repetitive practice and immediate self-correction.",{"@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/factorising-quadratic-equations-sheet-3/634672/",{"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/factorising-quadratic-equations-sheet-3/634672.png","ImageObject",300,407,{"name":92,"@type":93},"Taylor Morgan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-10-22",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What type of quadratic equations does this sheet focus on?","Question",{"text":112,"@type":113},"The sheet focuses on quadratic equations where the terms result in negative values within the brackets during the factorisation process.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How many problems are included in this practice set?",{"text":117,"@type":113},"There are 16 individual quadratic equations provided for practice, ranging from simple variables to those involving larger coefficients.",{"name":119,"@type":110,"acceptedAnswer":120},"Are the answers provided for these exercises?",{"text":121,"@type":113},"Yes, a complete answer key is included at the end of the document, showing the factored form and the corresponding roots for each of the 16 equations.","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},634672,1792887415,{"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":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"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":24},1099523885336,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","FACTORISING QUADRATIC EQUATIONS SHEET 3  \nFactorise these quadratic equations. Negative values inside each bracket.  \n\n| 1) | x2 – 4x + 3 = 0 | (x –   )(x –   ) | x =   or   |\n| --- | --- | --- | --- |\n| 2) | y2 – 7y + 10 = 0 |  |  |\n| 3) | z2 – 3z + 2 = 0 |  |  |\n| 4) | a2 – 5a + 6 = 0 |  |  |\n| 5) | b2 – 8b + 16 = 0 |  |  |\n| 6) | c2 – 6c + 8 = 0 |  |  |\n| 7) | d2 – 7d + 12 = 0 |  |  |\n| 8) | e2 – 10e + 9 = 0 |  |  |\n| 9) | f2 – 9f + 20 = 0 |  |  |\n| 10) | g2 – 6g + 9 = 0 |  |  |\n| 11) | h2 – 11h + 30 = 0 |  |  |\n| 12) | i2 – 10i + 24 = 0 |  |  |\n| 13) | j2 – 12j + 27 = 0 |  |  |\n| 14) | k2 – 9k + 18 = 0 |  |  |\n| 15) | m2 – 10m + 21 = 0 |  |  |\n| 16) | n2 – 12n + 35 = 0 |  |  |\n\nFACTORISING QUADRATIC EQUATIONS SHEET 3 ANSWERS  \n\n| 1) | x2 – 4x + 3 = 0 | (x – 3)(x – 1) | x = 1 or 3 |\n| --- | --- | --- | --- |\n| 2) | y2 – 7y + 10 = 0 | (y – 5)(y – 2) | y = 2 or 5 |\n| 3) | z2 – 3z + 2 = 0 | (z – 2)(z – 1) | z = 1 or 2 |\n| 4) | a2 – 5a + 6 = 0 | (a – 3)(a – 2) | a = 2 or 3 |\n| 5) | b2 – 8b + 16 = 0 | (b – 4)(b – 4) or (b – 4)2 | b = 4 |\n| 6) | c2 – 6c + 8 = 0 | (c – 4)(c – 2) | c = 2 or 4 |\n| 7) | d2 – 7d + 12 = 0 | (d – 4)(d – 3) | d = 3 or 4 |\n| 8) | e2 – 10e + 9 = 0 | (e – 9)(e – 1) | e = 1 or 9 |\n| 9) | f2 – 9f + 20 = 0 | (f – 5)(f – 4) | f = 4 or 5 |\n| 10) | g2 – 6g + 9 = 0 | (g – 3)(g – 3) or (g – 3)2 | g = 3 |\n| 11) | h2 – 11h + 30 = 0 | (h – 6)(h – 5) | h = 5 or 6 |\n| 12) | i2 – 10i + 24 = 0 | (i – 6)(i – 4) | i = 4 or 6 |\n| 13) | j2 – 12j + 27 = 0 | (j – 9)(j – 3) | j = 3 or 9 |\n| 14) | k2 – 9k + 18 = 0 | (k – 6)(k – 3) | k = 3 or 6 |\n| 15) | m2 – 10m + 21 = 0 | (m – 7)(m – 3) | m = 3 or 7 |\n| 16) | n2 – 12n + 35 = 0 | (n – 7)(n – 5) | n = 5 or 7 |","cbCairvfNNu2vVzU","https://ap.wps.com/l/cbCairvfNNu2vVzU","pdf",142164,"English","# Factorising Quadratic Equations Sheet 3\n## Practice Problems\n## Answer Key","[{\"question\":\"What type of quadratic equations does this sheet focus on?\",\"answer\":\"The sheet focuses on quadratic equations where the terms result in negative values within the brackets during the factorisation process.\"},{\"question\":\"How many problems are included in this practice set?\",\"answer\":\"There are 16 individual quadratic equations provided for practice, ranging from simple variables to those involving larger coefficients.\"},{\"question\":\"Are the answers provided for these exercises?\",\"answer\":\"Yes, a complete answer key is included at the end of the document, showing the factored form and the corresponding roots for each of the 16 equations.\"}]","Factorising Quadratic Equations - Sheet 3 | PDF",1792674268]