[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-493582-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-493582-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","the-vocabulary-of-polynomials-word-definition-combining-like-terms","The Vocabulary of Polynomials - Word & Definition - Combining Like Terms","","This document explains core vocabulary for polynomials in one variable, defining constant, variable, term, monomial, binomial, trinomial, polynomial, coefficient, and degrees of both terms and the whole polynomial. It then focuses on combining like terms by distinguishing like terms (same variable power) from unlike terms (different powers). Worked examples show how degrees and exponents remain unchanged while coefficients are added or subtracted, followed by practice questions about polynomial degree and polynomial addition.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/the-vocabulary-of-polynomials-word-definition-combining-like-terms/493582/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/the-vocabulary-of-polynomials-word-definition-combining-like-terms/493582.png","ImageObject",300,407,{"name":42,"@type":43},"pixelkiddo","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-29","2026-10-01",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",12,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the degree of a polynomial in one variable?","Question",{"text":63,"@type":64},"The degree of the polynomial is the greatest degree of any term in the polynomial. The degree of a term is the whole number exponent on the variable in that term.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"When can you combine polynomial terms?",{"text":68,"@type":64},"You can only add terms that are like terms. Like terms must have the same variable raised to the same power.",{"name":70,"@type":61,"acceptedAnswer":71},"How do you combine like terms?",{"text":72,"@type":64},"Add the coefficients while keeping the exponent on the variable the same as in each original term. The example shows 8x^2 + 5x^2 becoming (8 + 5)x^2.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},493582,1791729658,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":96,"preview_page_count":4},962090883892,"https://ap-avatar.wpscdn.com/avatar/e00115db34f3e0f11b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1790152879550218658","The Vocabulary of Polynomials (in one variable)  \nWord & Definition  \n􀁸 Constant: A fixed real number  \n􀁸 Variable: A letter used to represent a changeable number  \n􀁸 Term: A constant standing alone or a constant multiplied by a variable raised to a whole number power  \n􀁸 Monomial: A single term  \n􀁸 Binomial: A sum of two terms that cannot be combined  \n􀁸 Trinomial: A sum of three terms that cannot be combined  \n􀁸 Polynomial: A sum of any number of terms  \n􀁸 Coefficient: The constant number factor of a term  \n􀁸 Degree (of a term): The whole number exponent on the variable in a term  \n􀁸 Degree (of the polynomial): The greatest degree of any term in the polynomial  \nCombining Like Terms  \nPolynomial terms can only be added when they are “like terms”: they have the same variable raised to the same power. Consider these pairs of terms.  \nTerms & Like or Unlike?  \n􀁸 8􀝔2 , 5􀝔2 : Like terms; the variable 􀝔 is raised to the second power in both  \n􀁸 9􀝕3 , 4􀝕 : Unlike terms; the variable 􀝕 has different powers  \n􀁸 −23􀝔, 7􀝕 : Unlike terms; the variable 􀝕 has different powers  \n􀁸  3 􀝖 5 −6 5􀝖5 : Like terms; the variable 􀝖 is raised to the fifth power in both 4 , .  \nTo combine like terms, add the coefficients. Keep the exponent on the variable the same as in each of the original terms. For example  \n􀁸 8􀝔2 + 5􀝔2 = (8 + 5)􀝔 2 = 13􀝔2  \n􀁸 ~~ ~~34 􀝖 5 − 􀝖 5 = (34 − 1) 􀝖 5 = − 14 􀝖 5  \nFor more practice, see Add and Subtract Polynomials. Then answer the following questions.  \n1. What is the degree of the polynomial 4􀝕5 − 2􀝕7 + 8􀝕?  \n2. Add (􀝔3 + 7􀝔2 − 5􀝔 − 16) + (4􀝔3 − 3􀝔2 − 7􀝔 + 13)  \nThe link included here will take the reader to OpenStax Elementary Algebra, which is published under a Creative Commons Attribution License 4.0. Download for free at [http://cnx.org/contents/0889907c-f0ef-496a-bcb8-2a5bb121717f@8.17](http://cnx.org/contents/0889907c-f0ef-496a-bcb8-2a5bb121717f@8.17)  \nCentral Lakes College is committed to legal affirmative action, equal opportunity, access and diversity providing equal access to education for all students. Students who have a disability, or believe they may have a disability, are invited to contact the Accessibility Services at [accessibilityservices@clcmn.edu](accessibilityservices@clcmn.edu), 218-855-8175, or office E138 to determine eligibility and/or request accommodations. Accommodations are determined on a case-by-case basis.","cbCaibuCqv4ynqcj","https://ap.wps.com/l/cbCaibuCqv4ynqcj","pdf",663897,"English","# Word & Definition\n## Constant, Variable, Term, and Degree\n# Combining Like Terms\n## Like vs Unlike Terms\n## Adding Like Terms and Examples\n## Practice Questions","[{\"question\":\"What is the degree of a polynomial in one variable?\",\"answer\":\"The degree of the polynomial is the greatest degree of any term in the polynomial. The degree of a term is the whole number exponent on the variable in that term.\"},{\"question\":\"When can you combine polynomial terms?\",\"answer\":\"You can only add terms that are like terms. Like terms must have the same variable raised to the same power.\"},{\"question\":\"How do you combine like terms?\",\"answer\":\"Add the coefficients while keeping the exponent on the variable the same as in each original term. The example shows 8x^2 + 5x^2 becoming (8 + 5)x^2.\"}]","The Vocabulary of Polynomials - Word & Definition - Combining Like Terms | PDF",1790884233]