{"id":754,"date":"2021-09-15T19:24:04","date_gmt":"2021-09-15T19:24:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/?post_type=chapter&#038;p=754"},"modified":"2022-02-02T01:04:11","modified_gmt":"2022-02-02T01:04:11","slug":"8-2-evaluating-a-polynomial-for-given-values-of-the-variables","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/chapter\/8-2-evaluating-a-polynomial-for-given-values-of-the-variables\/","title":{"raw":"8.2: Evaluating a Polynomial for Given Values of the Variables","rendered":"8.2: Evaluating a Polynomial for Given Values of the Variables"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Evaluate a polynomial for a given value<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key words<\/h3>\r\n<ul>\r\n \t<li><strong>Evaluate<\/strong>: find the value of<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2 id=\"title2\">Evaluating a Polynomial<\/h2>\r\nPreviously we evaluated expressions by \"plugging in\" numbers for variables. Since polynomials are expressions, we'll follow the same procedures to evaluate polynomials\u2014substitute the given value for the variable into the polynomial, and then simplify.\u00a0 To evaluate an expression for a value of the variable, we substitute the value for the variable <i>every time<\/i> it appears. Then use the order of operations to find the resulting value for the expression.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nEvaluate [latex]3{x}^{2}-9x+7[\/latex] when\r\n\r\n1. [latex]x=3[\/latex]\r\n2. [latex]x=-1[\/latex]\r\n<h4>Solution<\/h4>\r\n<table id=\"eip-id1168468653511\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1. [latex]x=3[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3{x}^{2}-9x+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]3[\/latex] for [latex]x[\/latex]<\/td>\r\n<td>[latex]3{\\left(3\\right)}^{2}-9\\left(3\\right)+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the expression with the exponent.<\/td>\r\n<td>[latex]3\\cdot 9 - 9\\left(3\\right)+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]27 - 27+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]7[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469859387\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2. [latex]x=-1[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3{x}^{2}-9x+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]\u22121[\/latex] for [latex]x[\/latex]<\/td>\r\n<td>[latex]3{\\left(-1\\right)}^{2}-9\\left(-1\\right)+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the expression with the exponent.<\/td>\r\n<td>[latex]3\\cdot 1 - 9\\left(-1\\right)+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]3+9+7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]19[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nEvaluate [latex]3x^{2}-2x+1[\/latex] for [latex]x=-1[\/latex].\r\n\r\n&nbsp;\r\n<h4>Solution<\/h4>\r\nSubstitute [latex]-1[\/latex] for each [latex]x[\/latex] in the polynomial:\r\n<p style=\"text-align: center;\">[latex]3x^{2}-2x+1=3\\left(-1\\right)^{2}-2\\left(-1\\right)+1[\/latex]<\/p>\r\nFollowing the order of operations, evaluate exponents first:\r\n<p style=\"text-align: center;\">[latex]3\\left(1\\right)-2\\left(-1\\right)+1[\/latex]<\/p>\r\nMultiply from left to right:\r\n<p style=\"text-align: center;\">[latex]3+2+1[\/latex]<\/p>\r\nAdd:\r\n<p style=\"text-align: center;\">[latex]3+2+1[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]6[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]3x^{2}-2x+1=6[\/latex], for [latex]x=-1[\/latex]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nEvaluate [latex] \\displaystyle -\\frac{2}{3}p^{4}+2p^{3}-p[\/latex] for [latex]p = 3[\/latex].\r\n\r\n&nbsp;\r\n<h4>Solution<\/h4>\r\nSubstitute 3 for each <i>p<\/i> in the polynomial.\r\n<p style=\"text-align: center;\">[latex]\\displaystyle -\\frac{2}{3}p^{4}+2p^{3}-p=\\displaystyle -\\frac{2}{3}\\left(3\\right)^{4}+2\\left(3\\right)^{3}-(3)[\/latex]<\/p>\r\nFollowing the order of operations, evaluate exponents first:\r\n<p style=\"text-align: center;\">[latex] \\displaystyle -\\frac{2}{3}\\left(81\\right)+2\\left(27\\right)-3[\/latex]<\/p>\r\nMultiply:\r\n<p style=\"text-align: center;\">[latex]\\large -54 + 54 \u2013 3[\/latex]<\/p>\r\nAdd and then subtract:\r\n<p style=\"text-align: center;\">[latex]-3[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex] \\displaystyle -\\frac{2}{3}p^{4}+2p^{3}-p=-3[\/latex], for [latex]p = 3[\/latex]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146086[\/ohm_question]\r\n\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nThe following video presents examples of evaluating a polynomial for a given value.\r\n\r\nhttps:\/\/youtu.be\/2EeFrgQP1hM\r\n\r\nThe following video provides another example of how to evaluate a polynomial for a negative number.\r\n\r\nhttps:\/\/youtu.be\/c7XkBD0fszc\r\n\r\n&nbsp;\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\nEvaluate [latex]3x^2-6x+4[\/latex] when\u00a0[latex]x=-\\frac{2}{3}[\/latex]\r\n<h4>Solution<\/h4>\r\n<p style=\"text-align: center;\">[latex]\\begin{equation}\\begin{aligned}&amp;3x^2-6x+4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{substitute }x\\text{ with }-\\frac{2}{3}\\\\ &amp;= 3\\left ( -\\frac{2}{3}\\right )^2-6\\left ( -\\frac{2}{3}\\right )+4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{evaluate exponent}\\\\ &amp;= \\frac{3}{1}\\cdot \\frac{4}{9}-\\frac{6}{1}\\cdot -\\frac{2}{3}+4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{multiply}\\\\ &amp;=\\frac{4}{3}+4+4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{simplify}\\\\ &amp;=\\frac{4}{3}+\\frac{16}{1} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{add using a common denominator}\\\\ &amp;=\\frac{4+16\\cdot 3}{3} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{multiply}\\\\ &amp;= \\frac{4+48}{3}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{simplify}\\\\ &amp;= \\frac{52}{3}\\end{aligned}\\end{equation}[\/latex]<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nEvaluate [latex]x^3+4x^2[\/latex] when\u00a0[latex]x=-\\frac{1}{2}[\/latex]\r\n\r\n[reveal-answer q=\"hjm248\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"hjm248\"]\r\n\r\n[latex]\\frac{7}{8}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nEvaluate [latex]x^2+4x-2[\/latex] when\u00a0[latex]x=-\\frac{3}{8}[\/latex]\r\n\r\n[reveal-answer q=\"hjm531\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"hjm531\"]\r\n\r\n[latex]-\\frac{215}{64}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Evaluate a polynomial for a given value<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key words<\/h3>\n<ul>\n<li><strong>Evaluate<\/strong>: find the value of<\/li>\n<\/ul>\n<\/div>\n<h2 id=\"title2\">Evaluating a Polynomial<\/h2>\n<p>Previously we evaluated expressions by &#8220;plugging in&#8221; numbers for variables. Since polynomials are expressions, we&#8217;ll follow the same procedures to evaluate polynomials\u2014substitute the given value for the variable into the polynomial, and then simplify.\u00a0 To evaluate an expression for a value of the variable, we substitute the value for the variable <i>every time<\/i> it appears. Then use the order of operations to find the resulting value for the expression.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Evaluate [latex]3{x}^{2}-9x+7[\/latex] when<\/p>\n<p>1. [latex]x=3[\/latex]<br \/>\n2. [latex]x=-1[\/latex]<\/p>\n<h4>Solution<\/h4>\n<table id=\"eip-id1168468653511\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1. [latex]x=3[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]3{x}^{2}-9x+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]3[\/latex] for [latex]x[\/latex]<\/td>\n<td>[latex]3{\\left(3\\right)}^{2}-9\\left(3\\right)+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the expression with the exponent.<\/td>\n<td>[latex]3\\cdot 9 - 9\\left(3\\right)+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]27 - 27+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]7[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469859387\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2. [latex]x=-1[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]3{x}^{2}-9x+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]\u22121[\/latex] for [latex]x[\/latex]<\/td>\n<td>[latex]3{\\left(-1\\right)}^{2}-9\\left(-1\\right)+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the expression with the exponent.<\/td>\n<td>[latex]3\\cdot 1 - 9\\left(-1\\right)+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]3+9+7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]19[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Evaluate [latex]3x^{2}-2x+1[\/latex] for [latex]x=-1[\/latex].<\/p>\n<p>&nbsp;<\/p>\n<h4>Solution<\/h4>\n<p>Substitute [latex]-1[\/latex] for each [latex]x[\/latex] in the polynomial:<\/p>\n<p style=\"text-align: center;\">[latex]3x^{2}-2x+1=3\\left(-1\\right)^{2}-2\\left(-1\\right)+1[\/latex]<\/p>\n<p>Following the order of operations, evaluate exponents first:<\/p>\n<p style=\"text-align: center;\">[latex]3\\left(1\\right)-2\\left(-1\\right)+1[\/latex]<\/p>\n<p>Multiply from left to right:<\/p>\n<p style=\"text-align: center;\">[latex]3+2+1[\/latex]<\/p>\n<p>Add:<\/p>\n<p style=\"text-align: center;\">[latex]3+2+1[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]6[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]3x^{2}-2x+1=6[\/latex], for [latex]x=-1[\/latex]<\/p>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Evaluate [latex]\\displaystyle -\\frac{2}{3}p^{4}+2p^{3}-p[\/latex] for [latex]p = 3[\/latex].<\/p>\n<p>&nbsp;<\/p>\n<h4>Solution<\/h4>\n<p>Substitute 3 for each <i>p<\/i> in the polynomial.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle -\\frac{2}{3}p^{4}+2p^{3}-p=\\displaystyle -\\frac{2}{3}\\left(3\\right)^{4}+2\\left(3\\right)^{3}-(3)[\/latex]<\/p>\n<p>Following the order of operations, evaluate exponents first:<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle -\\frac{2}{3}\\left(81\\right)+2\\left(27\\right)-3[\/latex]<\/p>\n<p>Multiply:<\/p>\n<p style=\"text-align: center;\">[latex]\\large -54 + 54 \u2013 3[\/latex]<\/p>\n<p>Add and then subtract:<\/p>\n<p style=\"text-align: center;\">[latex]-3[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]\\displaystyle -\\frac{2}{3}p^{4}+2p^{3}-p=-3[\/latex], for [latex]p = 3[\/latex]<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146086\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146086&theme=oea&iframe_resize_id=ohm146086&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The following video presents examples of evaluating a polynomial for a given value.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Evaluate a Polynomial in One Variable\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/2EeFrgQP1hM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>The following video provides another example of how to evaluate a polynomial for a negative number.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Evaluate a Quadratic Expression With a Negative Value\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/c7XkBD0fszc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p>Evaluate [latex]3x^2-6x+4[\/latex] when\u00a0[latex]x=-\\frac{2}{3}[\/latex]<\/p>\n<h4>Solution<\/h4>\n<p style=\"text-align: center;\">[latex]\\begin{equation}\\begin{aligned}&3x^2-6x+4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{substitute }x\\text{ with }-\\frac{2}{3}\\\\ &= 3\\left ( -\\frac{2}{3}\\right )^2-6\\left ( -\\frac{2}{3}\\right )+4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{evaluate exponent}\\\\ &= \\frac{3}{1}\\cdot \\frac{4}{9}-\\frac{6}{1}\\cdot -\\frac{2}{3}+4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{multiply}\\\\ &=\\frac{4}{3}+4+4 \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{simplify}\\\\ &=\\frac{4}{3}+\\frac{16}{1} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{add using a common denominator}\\\\ &=\\frac{4+16\\cdot 3}{3} \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{multiply}\\\\ &= \\frac{4+48}{3}\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\text{simplify}\\\\ &= \\frac{52}{3}\\end{aligned}\\end{equation}[\/latex]<\/p>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Evaluate [latex]x^3+4x^2[\/latex] when\u00a0[latex]x=-\\frac{1}{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"qhjm248\">Show Answer<\/span><\/p>\n<div id=\"qhjm248\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\frac{7}{8}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Evaluate [latex]x^2+4x-2[\/latex] when\u00a0[latex]x=-\\frac{3}{8}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"qhjm531\">Show Answer<\/span><\/p>\n<div id=\"qhjm531\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]-\\frac{215}{64}[\/latex]<\/p>\n<\/div>\n<\/div>\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-754\">\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>Evaluate a Polynomial in One Variable. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/2EeFrgQP1hM\">https:\/\/youtu.be\/2EeFrgQP1hM<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Revision and Adaptation. <strong>Authored by<\/strong>: Hazel McKenna. <strong>Provided 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><li>Ex: Evaluate a Quadratic Expression with a Negative Value. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.youtube.com\/watch?v=c7XkBD0fszc&#038;t=7s\">https:\/\/www.youtube.com\/watch?v=c7XkBD0fszc&#038;t=7s<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Example: evaluate polynomial with fractional value; Try it hjm531; hjm248. <strong>Authored by<\/strong>: Hazel McKenna. <strong>Provided by<\/strong>: Utah Valley University. <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, Shared previously<\/div><ul class=\"citation-list\"><li>Unit 11: Exponents and Polynomials, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\">http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/<\/a>. <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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":422605,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Evaluate a Polynomial in One Variable\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/2EeFrgQP1hM\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 11: Exponents and Polynomials, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\" http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"Hazel McKenna\",\"organization\":\"Lumen 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