{"id":3648,"date":"2020-01-28T02:00:15","date_gmt":"2020-01-28T02:00:15","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3648"},"modified":"2021-02-05T23:50:05","modified_gmt":"2021-02-05T23:50:05","slug":"identifying-characteristics-of-polynomials","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/identifying-characteristics-of-polynomials\/","title":{"raw":"Identifying Characteristics of Polynomials","rendered":"Identifying Characteristics of Polynomials"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify whether a polynomial is a monomial, binomial, or trinomial<\/li>\r\n \t<li>Determine the degree of a polynomial<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Identify Polynomials, Monomials, Binomials, and Trinomials<\/h2>\r\nIn Evaluate, Simplify, and Translate Expressions, you learned that a term is a constant or the product of a constant and one or more variables. When it is of the form [latex]a{x}^{m}[\/latex], where [latex]a[\/latex] is a constant and [latex]m[\/latex] is a whole number, it is called a monomial. A monomial, or a sum and\/or difference of monomials, is called a polynomial.\r\n<div class=\"textbox shaded\">\r\n<h3>Polynomials<\/h3>\r\npolynomial\u2014A monomial, or two or more monomials, combined by addition or subtraction\r\nmonomial\u2014A polynomial with exactly one term\r\nbinomial\u2014 A polynomial with exactly two terms\r\ntrinomial\u2014A polynomial with exactly three terms\r\n\r\n<\/div>\r\nNotice the roots:\r\n<ul id=\"fs-id1485432\">\r\n \t<li><em>poly<\/em>- means many<\/li>\r\n \t<li><em>mono<\/em>- means one<\/li>\r\n \t<li><em>bi<\/em>- means two<\/li>\r\n \t<li><em>tri<\/em>- means three<\/li>\r\n<\/ul>\r\nHere are some examples of polynomials:\r\n<table id=\"fs-id1171105397687\" class=\"unnumbered column-header\" summary=\"The table has four rows and four columns. The first column lists Polynomial, Monomial, Binomial, and Trinomial. The columns list examples of each. The first row lists b plu 1, 4y squared minus 7y plus 2, and 5x to the fifth minus 4x to the fourth plus x cubed minus 9x plus 1. The second row lists 5, 4b squared, and negative9x cubed. The third row lists 3a minus 7, y squared minus 9, and 17x cubed plus 14x squared. The fourth row lists x squared minus 5x plus 6, 4y squared minus 7y plus 2, and 5a to the fourth minus 3a cubed plus a.\">\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td><strong>Polynomial<\/strong><\/td>\r\n<td>[latex]b+1[\/latex]<\/td>\r\n<td>[latex]4{y}^{2}-7y+2[\/latex]<\/td>\r\n<td>[latex]5{x}^{5}-4{x}^{4}+{x}^{3}+8{x}^{2}-9x+1[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Monomial<\/strong><\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>[latex]4{b}^{2}[\/latex]<\/td>\r\n<td>[latex]-9{x}^{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Binomial<\/strong><\/td>\r\n<td>[latex]3a - 7[\/latex]<\/td>\r\n<td>[latex]{y}^{2}-9[\/latex]<\/td>\r\n<td>[latex]17{x}^{3}+14{x}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Trinomial<\/strong><\/td>\r\n<td>[latex]{x}^{2}-5x+6[\/latex]<\/td>\r\n<td>[latex]4{y}^{2}-7y+2[\/latex]<\/td>\r\n<td>[latex]5{a}^{4}-3{a}^{3}+a[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that every monomial, binomial, and trinomial is also a polynomial. They are special members of the family of polynomials and so they have special names. We use the words \u2018monomial\u2019, \u2018binomial\u2019, and \u2018trinomial\u2019 when referring to these special polynomials and just call all the rest \u2018polynomials\u2019.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine whether each polynomial is a monomial, binomial, trinomial, or other polynomial:\r\n\r\n1. [latex]8{x}^{2}-7x - 9[\/latex]\r\n2. [latex]-5{a}^{4}[\/latex]\r\n3. [latex]{x}^{4}-7{x}^{3}-6{x}^{2}+5x+2[\/latex]\r\n4. [latex]11 - 4{y}^{3}[\/latex]\r\n5. [latex]n[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-118\" class=\"unnumbered unstyled\" summary=\".\">\r\n<thead>\r\n<tr>\r\n<th><\/th>\r\n<th>Polynomial<\/th>\r\n<th>Number of terms<\/th>\r\n<th>Type<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td>[latex]8{x}^{2}-7x - 9[\/latex]<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<td>Trinomial<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2.<\/td>\r\n<td>[latex]-5{a}^{4}[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>Monomial<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3.<\/td>\r\n<td>[latex]{x}^{4}-7{x}^{3}-6{x}^{2}+5x+2[\/latex]<\/td>\r\n<td>[latex]5[\/latex]<\/td>\r\n<td>Polynomial<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4.<\/td>\r\n<td>[latex]11 - 4{y}^{3}[\/latex]<\/td>\r\n<td>[latex]2[\/latex]<\/td>\r\n<td>Binomial<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5.<\/td>\r\n<td>[latex]n[\/latex]<\/td>\r\n<td>[latex]1[\/latex]<\/td>\r\n<td>Monomial<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146073[\/ohm_question]\r\n\r\n<\/div>\r\n<h3>Determine the Degree of Polynomials<\/h3>\r\nIn this section, we will work with polynomials that have only one variable in each term. The degree of a polynomial and the degree of its terms are determined by the exponents of the variable.\r\n\r\nA monomial that has no variable, just a constant, is a special case. The degree of a constant is [latex]0[\/latex] \u2014it has no variable.\r\n<div class=\"textbox shaded\">\r\n<h3>Degree of a Polynomial<\/h3>\r\nThe degree of a term is the exponent of its variable.\r\nThe degree of a constant is [latex]0[\/latex].\r\nThe degree of a polynomial is the highest degree of all its terms.\r\n\r\n<\/div>\r\nLet's see how this works by looking at several polynomials. We'll take it step by step, starting with monomials, and then progressing to polynomials with more terms.\r\n\r\nRemember: Any base written without an exponent has an implied exponent of [latex]1[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224331\/CNX_BMath_Figure_10_01_002.png\" alt=\"A table is shown. The top row is titled \" width=\"696\" height=\"523\" \/>\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the degree of the following polynomials:\r\n\r\n1. [latex]4x[\/latex]\r\n2. [latex]3{x}^{3}-5x+7[\/latex]\r\n3. [latex]-11[\/latex]\r\n4. [latex]-6{x}^{2}+9x - 3[\/latex]\r\n5. [latex]8x+2[\/latex]\r\n[reveal-answer q=\"162218\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"162218\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468469502\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td>[latex]4x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The exponent of [latex]x[\/latex] is one. [latex]x={x}^{1}[\/latex]<\/td>\r\n<td>The degree is [latex]1[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2.<\/td>\r\n<td>[latex]3{x}^{3}-5x+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The highest degree of all the terms is [latex]3[\/latex].<\/td>\r\n<td>The degree is [latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3.<\/td>\r\n<td>[latex]-11[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The degree of a constant is [latex]0[\/latex].<\/td>\r\n<td>The degree is [latex]0[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4.<\/td>\r\n<td>[latex]-6{x}^{2}+9x - 3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The highest degree of all the terms is [latex]2[\/latex].<\/td>\r\n<td>The degree is [latex]2[\/latex].<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>5.<\/td>\r\n<td>[latex]8x+2[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The highest degree of all the terms is [latex]1[\/latex].<\/td>\r\n<td>The degree is [latex]1[\/latex].<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nWorking with polynomials is easier when you list the terms in descending order of degrees. When a polynomial is written this way, it is said to be in standard form. Look back at the polynomials in the previous example. Notice that they are all written in standard form. Get in the habit of writing the term with the highest degree first.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146070[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Identify whether a polynomial is a monomial, binomial, or trinomial<\/li>\n<li>Determine the degree of a polynomial<\/li>\n<\/ul>\n<\/div>\n<h2>Identify Polynomials, Monomials, Binomials, and Trinomials<\/h2>\n<p>In Evaluate, Simplify, and Translate Expressions, you learned that a term is a constant or the product of a constant and one or more variables. When it is of the form [latex]a{x}^{m}[\/latex], where [latex]a[\/latex] is a constant and [latex]m[\/latex] is a whole number, it is called a monomial. A monomial, or a sum and\/or difference of monomials, is called a polynomial.<\/p>\n<div class=\"textbox shaded\">\n<h3>Polynomials<\/h3>\n<p>polynomial\u2014A monomial, or two or more monomials, combined by addition or subtraction<br \/>\nmonomial\u2014A polynomial with exactly one term<br \/>\nbinomial\u2014 A polynomial with exactly two terms<br \/>\ntrinomial\u2014A polynomial with exactly three terms<\/p>\n<\/div>\n<p>Notice the roots:<\/p>\n<ul id=\"fs-id1485432\">\n<li><em>poly<\/em>&#8211; means many<\/li>\n<li><em>mono<\/em>&#8211; means one<\/li>\n<li><em>bi<\/em>&#8211; means two<\/li>\n<li><em>tri<\/em>&#8211; means three<\/li>\n<\/ul>\n<p>Here are some examples of polynomials:<\/p>\n<table id=\"fs-id1171105397687\" class=\"unnumbered column-header\" summary=\"The table has four rows and four columns. The first column lists Polynomial, Monomial, Binomial, and Trinomial. The columns list examples of each. The first row lists b plu 1, 4y squared minus 7y plus 2, and 5x to the fifth minus 4x to the fourth plus x cubed minus 9x plus 1. The second row lists 5, 4b squared, and negative9x cubed. The third row lists 3a minus 7, y squared minus 9, and 17x cubed plus 14x squared. The fourth row lists x squared minus 5x plus 6, 4y squared minus 7y plus 2, and 5a to the fourth minus 3a cubed plus a.\">\n<tbody>\n<tr valign=\"top\">\n<td><strong>Polynomial<\/strong><\/td>\n<td>[latex]b+1[\/latex]<\/td>\n<td>[latex]4{y}^{2}-7y+2[\/latex]<\/td>\n<td>[latex]5{x}^{5}-4{x}^{4}+{x}^{3}+8{x}^{2}-9x+1[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Monomial<\/strong><\/td>\n<td>[latex]5[\/latex]<\/td>\n<td>[latex]4{b}^{2}[\/latex]<\/td>\n<td>[latex]-9{x}^{3}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Binomial<\/strong><\/td>\n<td>[latex]3a - 7[\/latex]<\/td>\n<td>[latex]{y}^{2}-9[\/latex]<\/td>\n<td>[latex]17{x}^{3}+14{x}^{2}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Trinomial<\/strong><\/td>\n<td>[latex]{x}^{2}-5x+6[\/latex]<\/td>\n<td>[latex]4{y}^{2}-7y+2[\/latex]<\/td>\n<td>[latex]5{a}^{4}-3{a}^{3}+a[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that every monomial, binomial, and trinomial is also a polynomial. They are special members of the family of polynomials and so they have special names. We use the words \u2018monomial\u2019, \u2018binomial\u2019, and \u2018trinomial\u2019 when referring to these special polynomials and just call all the rest \u2018polynomials\u2019.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine whether each polynomial is a monomial, binomial, trinomial, or other polynomial:<\/p>\n<p>1. [latex]8{x}^{2}-7x - 9[\/latex]<br \/>\n2. [latex]-5{a}^{4}[\/latex]<br \/>\n3. [latex]{x}^{4}-7{x}^{3}-6{x}^{2}+5x+2[\/latex]<br \/>\n4. [latex]11 - 4{y}^{3}[\/latex]<br \/>\n5. [latex]n[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-118\" class=\"unnumbered unstyled\" summary=\".\">\n<thead>\n<tr>\n<th><\/th>\n<th>Polynomial<\/th>\n<th>Number of terms<\/th>\n<th>Type<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1.<\/td>\n<td>[latex]8{x}^{2}-7x - 9[\/latex]<\/td>\n<td>[latex]3[\/latex]<\/td>\n<td>Trinomial<\/td>\n<\/tr>\n<tr>\n<td>2.<\/td>\n<td>[latex]-5{a}^{4}[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>Monomial<\/td>\n<\/tr>\n<tr>\n<td>3.<\/td>\n<td>[latex]{x}^{4}-7{x}^{3}-6{x}^{2}+5x+2[\/latex]<\/td>\n<td>[latex]5[\/latex]<\/td>\n<td>Polynomial<\/td>\n<\/tr>\n<tr>\n<td>4.<\/td>\n<td>[latex]11 - 4{y}^{3}[\/latex]<\/td>\n<td>[latex]2[\/latex]<\/td>\n<td>Binomial<\/td>\n<\/tr>\n<tr>\n<td>5.<\/td>\n<td>[latex]n[\/latex]<\/td>\n<td>[latex]1[\/latex]<\/td>\n<td>Monomial<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146073\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146073&theme=oea&iframe_resize_id=ohm146073&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h3>Determine the Degree of Polynomials<\/h3>\n<p>In this section, we will work with polynomials that have only one variable in each term. The degree of a polynomial and the degree of its terms are determined by the exponents of the variable.<\/p>\n<p>A monomial that has no variable, just a constant, is a special case. The degree of a constant is [latex]0[\/latex] \u2014it has no variable.<\/p>\n<div class=\"textbox shaded\">\n<h3>Degree of a Polynomial<\/h3>\n<p>The degree of a term is the exponent of its variable.<br \/>\nThe degree of a constant is [latex]0[\/latex].<br \/>\nThe degree of a polynomial is the highest degree of all its terms.<\/p>\n<\/div>\n<p>Let&#8217;s see how this works by looking at several polynomials. We&#8217;ll take it step by step, starting with monomials, and then progressing to polynomials with more terms.<\/p>\n<p>Remember: Any base written without an exponent has an implied exponent of [latex]1[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224331\/CNX_BMath_Figure_10_01_002.png\" alt=\"A table is shown. The top row is titled\" width=\"696\" height=\"523\" \/><\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the degree of the following polynomials:<\/p>\n<p>1. [latex]4x[\/latex]<br \/>\n2. [latex]3{x}^{3}-5x+7[\/latex]<br \/>\n3. [latex]-11[\/latex]<br \/>\n4. [latex]-6{x}^{2}+9x - 3[\/latex]<br \/>\n5. [latex]8x+2[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q162218\">Show Solution<\/span><\/p>\n<div id=\"q162218\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468469502\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td>[latex]4x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The exponent of [latex]x[\/latex] is one. [latex]x={x}^{1}[\/latex]<\/td>\n<td>The degree is [latex]1[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>2.<\/td>\n<td>[latex]3{x}^{3}-5x+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The highest degree of all the terms is [latex]3[\/latex].<\/td>\n<td>The degree is [latex]3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>3.<\/td>\n<td>[latex]-11[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The degree of a constant is [latex]0[\/latex].<\/td>\n<td>The degree is [latex]0[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>4.<\/td>\n<td>[latex]-6{x}^{2}+9x - 3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The highest degree of all the terms is [latex]2[\/latex].<\/td>\n<td>The degree is [latex]2[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>5.<\/td>\n<td>[latex]8x+2[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The highest degree of all the terms is [latex]1[\/latex].<\/td>\n<td>The degree is [latex]1[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Working with polynomials is easier when you list the terms in descending order of degrees. When a polynomial is written this way, it is said to be in standard form. Look back at the polynomials in the previous example. Notice that they are all written in standard form. Get in the habit of writing the term with the highest degree first.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146070\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146070&theme=oea&iframe_resize_id=ohm146070&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-3648\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146070, 146073. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":11,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146070, 146073\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3648","chapter","type-chapter","status-web-only","hentry"],"part":50,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3648","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3648\/revisions"}],"predecessor-version":[{"id":3649,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3648\/revisions\/3649"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/50"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3648\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3648"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3648"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3648"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}