[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-573820-105":53,"doc-detail-573820-en":120},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":113,"head_meta":115,"extra_data":117,"updated_unix":119},105,"en","algebra-1-cheat-sheet-polynomial-identities-and-factoring-guide","Algebra 1 Cheat Sheet - polynomial identities and factoring guide","","Algebra 1 Cheat Sheet compiles core algebra techniques into a quick reference format. It defines polynomials in standard form and classifies them by degree, then lists key factoring identities such as difference of two squares and cubes and sum of two cubes. The sheet also covers factoring and solution structures, polynomial long division and algebraic fractions, plus binomial coefficients and the binomial theorem for expanding (a + b)^n. It concludes with algebraic identities, formula manipulation rules, and stepwise methods for solving linear equations and systems.",{"@graph":63,"@context":112},[64,80,95],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/algebra-1-cheat-sheet-polynomial-identities-and-factoring-guide/573820/",4,{"url":78,"name":59,"@type":81,"author":82,"headline":59,"publisher":85,"fileFormat":88,"inLanguage":57,"description":61,"dateModified":89,"datePublished":89,"encodingFormat":88,"isAccessibleForFree":90,"interactionStatistic":91},"DigitalDocument",{"name":83,"@type":84},"Chumphorn","Person",{"url":68,"name":86,"@type":87},"DocShare","Organization","application/pdf","2026-10-14",true,{"@type":92,"interactionType":93,"userInteractionCount":4},"InteractionCounter",{"@type":94},"ViewAction",{"@type":96,"mainEntity":97},"FAQPage",[98,104,108],{"name":99,"@type":100,"acceptedAnswer":101},"How do you write a polynomial in standard form?","Question",{"text":102,"@type":103},"A polynomial is written as ax^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 with coefficients a_i in R and n a natural number. The sheet presents this structure as the standard expression.","Answer",{"name":105,"@type":100,"acceptedAnswer":106},"What identities are commonly used for factoring?",{"text":107,"@type":103},"It lists difference of two squares, difference of two cubes, and sum of two cubes. These are given in factored form, such as a^2 - b^2 = (a + b)(a - b) and a^3 + b^3 = (a + b)(a^2 - ab + b^2).",{"name":109,"@type":100,"acceptedAnswer":110},"What are the basic steps for solving linear equations?",{"text":111,"@type":103},"The sheet states that you solve by making x the subject of the equation. It demonstrates reducing the equation step by step, isolating x, and checking the solution before finalizing.","https://schema.org",{"og:url":78,"og:type":114,"og:title":59,"og:site_name":86,"og:description":61},"article",{"robots":116,"canonical":78},"index,follow",{"doc_id":118,"site_id":56},573820,1791947476,{"code":4,"msg":5,"data":121},{"doc_id":118,"user_id":122,"nickname":83,"user_avatar":123,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":124,"file_id":125,"file_url":126,"file_type":127,"file_size":128,"view_count":4,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":9,"language":129,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":130,"faqs":131,"seo_title":132,"seo_description":61,"update_tm":119,"read_time":4},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","Algebra 1 Cheat Sheet  \nPolynomial  \nAn expression of the form:  \nax xn + an􀀀1xn􀀀1 + 􀀁 􀀁 􀀁 + a2 x2 + a 1 x + a0 Where ai 2 R; i = 0 ; 1 ; 2; : : : ; n; n 2 N.  \n Types Of Polynomials   \nLinear (degree  \n1)  \nax + b  \nQuadratic (degree 2) ax2 + bx + c  \nCubic (degree 3) ax3 + bx2 + cx + d  \n\n| Di􀀋erence Of Two Squares | a2 􀀀 b2 = (a + b)(a 􀀀 b) |\n| --- | --- |\n| Di􀀋erence Of Two Cubes | a3 􀀀b3 = (a􀀀b)(a2 +ab+b2 ) |\n| Sum Of Two Cubes | a3 +b3 = (a+b)(a2 􀀀ab+b2 ) |\n\nFactoring  \n(x3 + x2 􀀀 2x) 􀀄 (x 􀀀 1)  \nSolution:  \nx2 + 2x  \nx 􀀀 1 􀀁 x3 + x2 􀀀 2x  \n􀀀 x3 + x2  \n2x2 􀀀 2x 􀀀 2x2 + 2x  \n0  \na ( bc ) = abc ~~ ~~(~~ ab~~c~~ ~~) = abc  \n a  = ac  ( ~~a~~b) = ad  \n( ~~b~~c ) b ( ~~c~~d ) bc  \nab + cd = ad~~ ~~+bd~~ ~~bc ~~ ~~a~~ ~~+c~~ ~~b = ac + bc ab + ac  \n= b + c; a  0 a  \nPolynomial Long Division  \nAlgebraic Fractions  \nBinomial Coe􀀎cient  \nThe binomial coe􀀎cient represents the number of ways you can choose r objects from a group of n objects.  \n􀀒nr􀀓 = r!(nn􀀀!~~ ~~r)! 􀀒nr􀀓 = 􀀒n  r􀀓  \n􀀒nr􀀓 = n~~ ~~(n~~ ~~􀀀~~ ~~1k()k(n􀀀􀀀12)()k:~~ ~~:~~ ~~(n2)~~ ~~:~~ ~~:(k1~~ ~~􀀀~~ ~~1))  \n\n| \u003Cbr>Binomial Theorem\u003Cbr>For any positive integer n, |  |\n| --- | --- |\n| n (a + b)n = X\u003Cbr>m=0 | 􀀒nm􀀓 an􀀀mbn |\n| = 􀀒n0􀀓 an + 􀀒n1􀀓 an􀀀1b 1 + 􀀁 􀀁 􀀁 + 􀀒nn􀀓 bn |  |\n\nAlgebraic Identities  \nIn an identity, all coe􀀎cients of like powers are equal.  \nAn identity must be true for all values of the independent variables  \nExample: 3x + 7 = ax + b implies a = 3 and b = 7 .  \n\n| \u003Cbr>Manipulating Formulae\u003Cbr>What you do to one side of an equation, you must do to the other.\u003Cbr>In terms of x Write with x as the inde\u003Cbr>pendent variable\u003Cbr>The subject of Make it on it's own on one side of the equation |  |\n| --- | --- |\n| As a function of | same as 'in terms of' |\n\nSolving Linear Equations  \nLinear equations can be solved by making x with subject of the equation.  \nExample: Solve 4x + 2 = 14  \n4x + 2 = 14  \n=) 4x = 14 􀀀 2 = 12  \n12 =) x = = 3  \n4  \n\n|  |\n| --- |\n| 1. Reduce the three equations to two by eliminating one of the unknowns.\u003Cbr>2. Choose an unknown to isolate.\u003Cbr>3. Eliminate this unknown from all three equations, taking them two at a time.\u003Cbr>4. Solve these two equations.\u003Cbr>5. Use the solutions as values in the original equations\u003Cbr>6. Check your solution! |\n\nSystems of Equations With Three Variables","cbCailfshrvBqkWD","https://ap.wps.com/l/cbCailfshrvBqkWD","pdf",160343,"English","# Polynomial\n## Types of Polynomials\n# Difference of Two Squares and Cubes\n# Factoring\n# Polynomial Long Division and Algebraic Fractions\n# Binomial Coefficient and Binomial Theorem\n# Algebraic Identities\n# Manipulating Formulae\n# Solving Linear Equations\n# Systems of Equations With Three Variables","[{\"question\":\"How do you write a polynomial in standard form?\",\"answer\":\"A polynomial is written as ax^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 with coefficients a_i in R and n a natural number. The sheet presents this structure as the standard expression.\"},{\"question\":\"What identities are commonly used for factoring?\",\"answer\":\"It lists difference of two squares, difference of two cubes, and sum of two cubes. These are given in factored form, such as a^2 - b^2 = (a + b)(a - b) and a^3 + b^3 = (a + b)(a^2 - ab + b^2).\"},{\"question\":\"What are the basic steps for solving linear equations?\",\"answer\":\"The sheet states that you solve by making x the subject of the equation. It demonstrates reducing the equation step by step, isolating x, and checking the solution before finalizing.\"}]","Algebra 1 Cheat Sheet - polynomial identities and factoring guide | PDF"]