{"id":3652,"date":"2020-01-28T02:04:18","date_gmt":"2020-01-28T02:04:18","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3652"},"modified":"2020-01-28T02:06:10","modified_gmt":"2020-01-28T02:06:10","slug":"evaluating-a-polynomial-for-a-given-value","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/evaluating-a-polynomial-for-a-given-value\/","title":{"raw":"Evaluating a Polynomial for a Given Value","rendered":"Evaluating a Polynomial for a Given Value"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Evaluate a polynomial for integer values<\/li>\r\n<\/ul>\r\n<\/div>\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.\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\r\nSolution\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&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146086[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video provides another example of how to evaluate a quadratic polynomial for a negative number.\r\n\r\nhttps:\/\/youtu.be\/c7XkBD0fszc\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nThe polynomial [latex]-16{t}^{2}+300[\/latex] gives the height of an object [latex]t[\/latex] seconds after it is dropped from a [latex]300[\/latex] foot tall bridge. Find the height after [latex]t=3[\/latex] seconds.\r\n[reveal-answer q=\"237305\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"237305\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468766754\" class=\"unnumbered unstyled\" summary=\"The top line says negative 16 t squared plus 300. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-16t^2+300[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute [latex]3[\/latex] for [latex]t[\/latex]<\/td>\r\n<td>[latex]-16(\\color{red}{3})^2+300[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the expression with the exponent.<\/td>\r\n<td>[latex]-16\\cdot{9}+300[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-144+300[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]156[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146088[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Evaluate a polynomial for integer values<\/li>\n<\/ul>\n<\/div>\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.<\/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<p>Solution<\/p>\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<p>&nbsp;<\/p>\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>The following video provides another example of how to evaluate a quadratic polynomial for a negative number.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" 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<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>The polynomial [latex]-16{t}^{2}+300[\/latex] gives the height of an object [latex]t[\/latex] seconds after it is dropped from a [latex]300[\/latex] foot tall bridge. Find the height after [latex]t=3[\/latex] seconds.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q237305\">Show Solution<\/span><\/p>\n<div id=\"q237305\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468766754\" class=\"unnumbered unstyled\" summary=\"The top line says negative 16 t squared plus 300. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]-16t^2+300[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute [latex]3[\/latex] for [latex]t[\/latex]<\/td>\n<td>[latex]-16(\\color{red}{3})^2+300[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the expression with the exponent.<\/td>\n<td>[latex]-16\\cdot{9}+300[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-144+300[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]156[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146088\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146088&theme=oea&iframe_resize_id=ohm146088&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-3652\">\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 146088, 146087. <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, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Evaluate a Quadratic Expression With a Negative Value. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/c7XkBD0fszc\">https:\/\/youtu.be\/c7XkBD0fszc<\/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 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":13,"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 146088, 146087\",\"author\":\"Lumen 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