[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-634665-en":3,"doc-seo-634665-105":31,"detail-sidebar-cat-0-en-105":97},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},634665,1099523885336,"Taylor Morgan","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",4,"Exam","Factorising Quadratic Equations - Sheet 1","This document provides a structured educational exercise focused on factorising quadratic equations with positive coefficients. It presents sixteen algebraic problems involving a variety of variables, designed to help students practice identifying binomial factors. The content includes a dedicated practice worksheet followed by a comprehensive answer key that demonstrates the step-by-step process of breaking down quadratic expressions into their linear factors and solving for the unknown variables. The material is suitable for students learning introductory algebra and mastering the process of solving quadratic equations through factoring methods, specifically those resulting in integer solutions. By systematically working through these problems, learners can reinforce their understanding of mathematical patterns related to quadratic expansion and factorisation.","FACTORISING QUADRATIC EQUATIONS SHEET 1  \nFactorise these quadratic equations. Positive values only.  \n\n| 1) | x2 + 3x + 2 = 0 | x 2 + 2x + x + 2 = (x + 2)(x + 1) | x = -2 or-1 |\n| --- | --- | --- | --- |\n| 2) | a2 + 7a + 6 = 0 |  |  |\n| 3) | b2 + 4b + 4 = 0 |  |  |\n| 4) | c2 + 5c + 6 = 0 |  |  |\n| 5) | d2 + 8d + 12 = 0 |  |  |\n| 6) | e2 + 6e + 8 = 0 |  |  |\n| 7) | f2 + 7f + 10 = 0 |  |  |\n| 8) | g2 + 8g + 7 = 0 |  |  |\n| 9) | h2 + 10h + 9 = 0 |  |  |\n| 10) | i2 + 8i + 16 = 0 |  |  |\n| 11) | j2 + 7j + 12 = 0 |  |  |\n| 12) | k2 + 10k + 16 = 0 |  |  |\n| 13) | m2 + 8m + 15 = 0 |  |  |\n| 14) | n2 + 12n + 20 = 0 |  |  |\n| 15) | p2 + 9p + 18 = 0 |  |  |\n| 16) | q2 + 12q + 32 = 0 |  |  |\n\nFACTORISING QUADRATIC EQUATIONS SHEET 1 ANSWERS  \n\n| 1) | x2 + 3x + 2 = 0 | x 2 + 2x + x + 2 = (x + 2)(x + 1) | x = -2 or-1 |\n| --- | --- | --- | --- |\n| 2) | a2 + 7a + 6 = 0 | (a + 6)(a + 1) | a = -6 or-1 |\n| 3) | b2 + 4b + 4 = 0 | (b + 2)(b + 2) or (b + 2)2 | b = -2 |\n| 4) | c2 + 5c + 6 = 0 | (c + 3)(c + 2) | c = -3 or-2 |\n| 5) | d2 + 8d + 12 = 0 | (d + 6)(d + 2) | d = -6 or-2 |\n| 6) | e2 + 6e + 8 = 0 | (e + 4)(e + 2) | e = -4 or-2 |\n| 7) | f2 + 7f + 10 = 0 | (f + 5)(f + 2) | f = -5 or-2 |\n| 8) | g2 + 8g + 7 = 0 | (g + 7)(g + 1) | g = -7 or-1 |\n| 9) | h2 + 10h + 9 = 0 | (h + 9)(h + 1) | h = -9 or-1 |\n| 10) | i2 + 8i + 16 = 0 | (i + 4)(i + 4) or (i + 4)2 | i = -4 |\n| 11) | j2 + 7j + 12 = 0 | (j + 4)(j + 3) | j = -4 or-3 |\n| 12) | k2 + 10k + 16 = 0 | (k + 8)(k + 2) | k = -8 or-2 |\n| 13) | m2 + 8m + 15 = 0 | (m + 5)(m + 3) | m = -5 or-3 |\n| 14) | n2 + 12n + 20 = 0 | (n + 10)(n + 2) | n = -10 or-2 |\n| 15) | p2 + 9p + 18 = 0 | (p + 6)(p + 3) | p = -6 or-3 |\n| 16) | q2 + 12q + 32 = 0 | (q + 8)(q + 4) | q = -8 or-4 |","cbCaiuLQEjzMDqiM","https://ap.wps.com/l/cbCaiuLQEjzMDqiM","pdf",162624,6,1,2,"English","en",105,"# Factorising Quadratic Equations Practice Sheet\n## Answer Key","[{\"question\":\"What is the primary objective of this worksheet?\",\"answer\":\"The objective is to practice factorising quadratic equations that contain positive values and finding the solutions for the variables.\"},{\"question\":\"How are the solutions presented for equations with identical factors?\",\"answer\":\"When an equation has identical factors, such as (b+2)(b+2), it is represented as (b+2)² and results in a single solution for the variable.\"},{\"question\":\"Does this sheet cover quadratic equations with negative solutions?\",\"answer\":\"Yes, although the coefficients in the initial equations are positive, the solutions for the variables are negative integers, as shown in the provided answer key.\"}]","Factorising Quadratic Equations - 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