{"id":57,"date":"2023-06-21T13:22:28","date_gmt":"2023-06-21T13:22:28","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/the-distributive-property\/"},"modified":"2023-08-07T01:34:23","modified_gmt":"2023-08-07T01:34:23","slug":"the-distributive-property","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/the-distributive-property\/","title":{"raw":"RP2.1   Identify and Evaluate Polynomials","rendered":"RP2.1   Identify and Evaluate Polynomials"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Identify a polynomial<\/li>\r\n \t<li>Evaluate a polynomial for given values<\/li>\r\n<\/ul>\r\n<\/div>\r\nA polynomial is an expression consisting of a sum or difference of terms in which each term consists of a\u00a0real\u00a0number, a variable, or the product of a\u00a0real\u00a0number and one or more variables with non-negative integer exponents. Non negative integers are\u00a0[latex]0, 1, 2, 3, 4[\/latex], ...\r\n<h2>Identify a polynomial<\/h2>\r\nThe following table is intended to help you tell the difference between what is a polynomial and what is not.\r\n<table>\r\n<thead>\r\n<tr>\r\n<td>IS a Polynomial<\/td>\r\n<td>Is NOT a Polynomial<\/td>\r\n<td>Because<\/td>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>[latex]2x^2-\\frac{1}{2}x -9[\/latex]<\/td>\r\n<td>[latex]\\frac{2}{x^{2}}+x[\/latex]<\/td>\r\n<td>Polynomials only have variables in the numerator<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\frac{y}{4}-y^3[\/latex]<\/td>\r\n<td>[latex]\\frac{2}{y}+4[\/latex]<\/td>\r\n<td>Polynomials only have variables in the numerator<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\sqrt{12}\\left(a\\right)+9[\/latex]<\/td>\r\n<td>\u00a0[latex]\\sqrt{a}+7[\/latex]<\/td>\r\n<td>Roots are equivalent to rational exponents, and polynomials only have integer exponents<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe basic building block of a polynomial is a <b>monomial<\/b>. A monomial is one term and can be a number, a variable, or the product of a number and variables with an exponent. The number part of the term is called the <b>coefficient<\/b>.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/06\/01183539\/image003.jpg\" alt=\"The expression 6x to the power of 3. 6 is the coefficient, x is the variable, and the power of 3 is the exponent.\" width=\"183\" height=\"82\" \/>\r\n\r\nA polynomial containing two terms, such as [latex]2x - 9[\/latex], is called a <strong>binomial<\/strong>. A polynomial containing three terms, such as [latex]-3{x}^{2}+8x - 7[\/latex], is called a <strong>trinomial<\/strong>.\r\n\r\nWe can find the <strong>degree<\/strong> of a polynomial by identifying the highest power of the variable that occurs in the polynomial. The term with the highest degree is called the <strong>leading term<\/strong> because it is usually written first. The coefficient of the leading term is called the <strong>leading coefficient<\/strong>. When a polynomial is written so that the powers are descending, we say that it is in standard form. It is important to note that polynomials only have integer exponents.\r\n\r\n<img class=\"wp-image-2550 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/07\/15150341\/Screen-Shot-2016-07-15-at-8.03.13-AM-300x150.png\" alt=\"4x^3 - 9x^2 + 6x, with the text &quot;degree = 3&quot; and an arrow pointing at the exponent on x^3, and the text &quot;leading term =4&quot; with an arrow pointing at the 4. \" width=\"504\" height=\"252\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWhich of the following expressions is a polynomial? Select all that apply.\r\n<ol>\r\n \t<li style=\"list-style-type: none;\">\r\n<ol>\r\n \t<li>[latex]-\\frac{1}{12}{x}^{3}+5+2{x}^{2}[\/latex]<\/li>\r\n \t<li>[latex]5{x}^{\\frac{1}{2}}-2{x}^{3}+7x[\/latex]<\/li>\r\n \t<li>[latex]7p-{p}^{11}-1[\/latex]<\/li>\r\n \t<li>[latex]{x}^{-1}+{x}^{3}-9[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"626080\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"626080\"]\r\n<ol>\r\n \t<li>[latex]-\\frac{1}{12}{x}^{3}+5+2{x}^{2}[\/latex] is a polynomial.<\/li>\r\n \t<li>[latex]5{x}^{\\frac{1}{2}}-2{x}^{3}+7x[\/latex] is not a polynomial because it contains a non-integer exponent.<\/li>\r\n \t<li>[latex]7p-{p}^{11}-1[\/latex] is a polynomial.<\/li>\r\n \t<li>[latex]{x}^{-1}+{x}^{3}-9[\/latex] is not a polynomial because it contains a negative exponent.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe table below illustrates some examples of monomials, binomials, trinomials, and other polynomials. They are all written in standard form.\r\n<table style=\"border-spacing: 0px;\" border=\"1\" cellpadding=\"0\">\r\n<tbody>\r\n<tr>\r\n<td><b>Monomials<\/b><\/td>\r\n<td><b>Binomials<\/b><\/td>\r\n<td><b>Trinomials<\/b><\/td>\r\n<td><b>Other Polynomials<\/b><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]15[\/latex]<\/td>\r\n<td>[latex]3y+13[\/latex]<\/td>\r\n<td>[latex]x^{3}-x^{2}+1[\/latex]<\/td>\r\n<td>[latex]5x^{4}+3x^{3}-6x^{2}+2x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex] \\displaystyle \\frac{1}{2}x[\/latex]<\/td>\r\n<td>[latex]4p-7[\/latex]<\/td>\r\n<td>[latex]3x^{2}+2x-9[\/latex]<\/td>\r\n<td>[latex]\\frac{1}{3}x^{5}-2x^{4}+\\frac{2}{9}x^{3}-x^{2}+4x-\\frac{5}{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]-4y^{3}[\/latex]<\/td>\r\n<td>[latex]3x^{2}+\\frac{5}{8}x[\/latex]<\/td>\r\n<td>[latex]3y^{3}+y^{2}-2[\/latex]<\/td>\r\n<td>[latex]3t^{3}-3t^{2}-3t-3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]16n^{4}[\/latex]<\/td>\r\n<td>[latex]14y^{3}+3y[\/latex]<\/td>\r\n<td>[latex]a^{7}+2a^{5}-3a^{3}[\/latex]<\/td>\r\n<td>[latex]q^{7}+2q^{5}-3q^{3}+q[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWhen the coefficient of a polynomial term is\u00a0[latex]0[\/latex], you usually do not write the term at all (because\u00a0[latex]0[\/latex] times anything is\u00a0[latex]0[\/latex], and adding\u00a0[latex]0[\/latex] doesn\u2019t change the value). The last binomial above could be written as a trinomial, [latex]14y^{3}+0y^{2}+3y[\/latex].\r\n\r\nA term without a variable is called a <b>constant <\/b>term, and the degree of that term is\u00a0[latex]0[\/latex]. For example\u00a0[latex]13[\/latex] is the constant term in [latex]3y+13[\/latex]. You would usually say that [latex]14y^{3}+3y[\/latex] has no constant term or that the constant term is\u00a0[latex]0[\/latex].\r\n\r\nThe following video illustrates how to identify which expressions are polynomials.\r\nhttps:\/\/youtu.be\/nPAqfuoSbPI\r\n<h2>Evaluate a polynomial<\/h2>\r\nYou can evaluate polynomials just as you can other kinds of expressions. To evaluate an expression for a value of the variable, you 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=\"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[reveal-answer q=\"280466\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"280466\"]Substitute [latex]-1[\/latex] for each <i>x<\/i> in the polynomial.\r\n<p style=\"text-align: center;\">[latex]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\u00a0[latex]3[\/latex] times\u00a0[latex]1[\/latex], and then multiply [latex]-2[\/latex] times [latex]-1[\/latex].\r\n<p style=\"text-align: center;\">[latex]3+\\left(-2\\right)\\left(-1\\right)+1[\/latex]<\/p>\r\nChange the subtraction to addition of the opposite.\r\n<p style=\"text-align: center;\">[latex]3+2+1[\/latex]<\/p>\r\nFind the sum.\r\n<h4>Answer<\/h4>\r\n[latex]3x^{2}-2x+1=6[\/latex], for [latex]x=-1[\/latex]\r\n\r\n[\/hidden-answer]\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[reveal-answer q=\"745542\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"745542\"]Substitute\u00a0[latex]3[\/latex] for each <i>p<\/i> in the polynomial.\r\n<p style=\"text-align: center;\">[latex] \\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 and then multiply.\r\n<p style=\"text-align: center;\">[latex] \\displaystyle -\\frac{2}{3}\\left(81\\right)+2\\left(27\\right)-3[\/latex]<\/p>\r\nAdd and then subtract to get [latex]-3[\/latex].\r\n<p style=\"text-align: center;\">[latex]-54 + 54 \u2013 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[\/hidden-answer]\r\n\r\n<\/div>\r\n<p class=\"no-indent\" style=\"text-align: left;\">\u00a0In the following video we show more examples of evaluating polynomials for given values of the variable.<\/p>\r\nhttps:\/\/youtu.be\/2EeFrgQP1hM","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Identify a polynomial<\/li>\n<li>Evaluate a polynomial for given values<\/li>\n<\/ul>\n<\/div>\n<p>A polynomial is an expression consisting of a sum or difference of terms in which each term consists of a\u00a0real\u00a0number, a variable, or the product of a\u00a0real\u00a0number and one or more variables with non-negative integer exponents. Non negative integers are\u00a0[latex]0, 1, 2, 3, 4[\/latex], &#8230;<\/p>\n<h2>Identify a polynomial<\/h2>\n<p>The following table is intended to help you tell the difference between what is a polynomial and what is not.<\/p>\n<table>\n<thead>\n<tr>\n<td>IS a Polynomial<\/td>\n<td>Is NOT a Polynomial<\/td>\n<td>Because<\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>[latex]2x^2-\\frac{1}{2}x -9[\/latex]<\/td>\n<td>[latex]\\frac{2}{x^{2}}+x[\/latex]<\/td>\n<td>Polynomials only have variables in the numerator<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\frac{y}{4}-y^3[\/latex]<\/td>\n<td>[latex]\\frac{2}{y}+4[\/latex]<\/td>\n<td>Polynomials only have variables in the numerator<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\sqrt{12}\\left(a\\right)+9[\/latex]<\/td>\n<td>\u00a0[latex]\\sqrt{a}+7[\/latex]<\/td>\n<td>Roots are equivalent to rational exponents, and polynomials only have integer exponents<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The basic building block of a polynomial is a <b>monomial<\/b>. A monomial is one term and can be a number, a variable, or the product of a number and variables with an exponent. The number part of the term is called the <b>coefficient<\/b>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/06\/01183539\/image003.jpg\" alt=\"The expression 6x to the power of 3. 6 is the coefficient, x is the variable, and the power of 3 is the exponent.\" width=\"183\" height=\"82\" \/><\/p>\n<p>A polynomial containing two terms, such as [latex]2x - 9[\/latex], is called a <strong>binomial<\/strong>. A polynomial containing three terms, such as [latex]-3{x}^{2}+8x - 7[\/latex], is called a <strong>trinomial<\/strong>.<\/p>\n<p>We can find the <strong>degree<\/strong> of a polynomial by identifying the highest power of the variable that occurs in the polynomial. The term with the highest degree is called the <strong>leading term<\/strong> because it is usually written first. The coefficient of the leading term is called the <strong>leading coefficient<\/strong>. When a polynomial is written so that the powers are descending, we say that it is in standard form. It is important to note that polynomials only have integer exponents.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2550 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/07\/15150341\/Screen-Shot-2016-07-15-at-8.03.13-AM-300x150.png\" alt=\"4x^3 - 9x^2 + 6x, with the text &quot;degree = 3&quot; and an arrow pointing at the exponent on x^3, and the text &quot;leading term =4&quot; with an arrow pointing at the 4.\" width=\"504\" height=\"252\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Which of the following expressions is a polynomial? Select all that apply.<\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol>\n<li>[latex]-\\frac{1}{12}{x}^{3}+5+2{x}^{2}[\/latex]<\/li>\n<li>[latex]5{x}^{\\frac{1}{2}}-2{x}^{3}+7x[\/latex]<\/li>\n<li>[latex]7p-{p}^{11}-1[\/latex]<\/li>\n<li>[latex]{x}^{-1}+{x}^{3}-9[\/latex]<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q626080\">Show Solution<\/span><\/p>\n<div id=\"q626080\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]-\\frac{1}{12}{x}^{3}+5+2{x}^{2}[\/latex] is a polynomial.<\/li>\n<li>[latex]5{x}^{\\frac{1}{2}}-2{x}^{3}+7x[\/latex] is not a polynomial because it contains a non-integer exponent.<\/li>\n<li>[latex]7p-{p}^{11}-1[\/latex] is a polynomial.<\/li>\n<li>[latex]{x}^{-1}+{x}^{3}-9[\/latex] is not a polynomial because it contains a negative exponent.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>The table below illustrates some examples of monomials, binomials, trinomials, and other polynomials. They are all written in standard form.<\/p>\n<table style=\"border-spacing: 0px;\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td><b>Monomials<\/b><\/td>\n<td><b>Binomials<\/b><\/td>\n<td><b>Trinomials<\/b><\/td>\n<td><b>Other Polynomials<\/b><\/td>\n<\/tr>\n<tr>\n<td>[latex]15[\/latex]<\/td>\n<td>[latex]3y+13[\/latex]<\/td>\n<td>[latex]x^{3}-x^{2}+1[\/latex]<\/td>\n<td>[latex]5x^{4}+3x^{3}-6x^{2}+2x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\displaystyle \\frac{1}{2}x[\/latex]<\/td>\n<td>[latex]4p-7[\/latex]<\/td>\n<td>[latex]3x^{2}+2x-9[\/latex]<\/td>\n<td>[latex]\\frac{1}{3}x^{5}-2x^{4}+\\frac{2}{9}x^{3}-x^{2}+4x-\\frac{5}{6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]-4y^{3}[\/latex]<\/td>\n<td>[latex]3x^{2}+\\frac{5}{8}x[\/latex]<\/td>\n<td>[latex]3y^{3}+y^{2}-2[\/latex]<\/td>\n<td>[latex]3t^{3}-3t^{2}-3t-3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]16n^{4}[\/latex]<\/td>\n<td>[latex]14y^{3}+3y[\/latex]<\/td>\n<td>[latex]a^{7}+2a^{5}-3a^{3}[\/latex]<\/td>\n<td>[latex]q^{7}+2q^{5}-3q^{3}+q[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When the coefficient of a polynomial term is\u00a0[latex]0[\/latex], you usually do not write the term at all (because\u00a0[latex]0[\/latex] times anything is\u00a0[latex]0[\/latex], and adding\u00a0[latex]0[\/latex] doesn\u2019t change the value). The last binomial above could be written as a trinomial, [latex]14y^{3}+0y^{2}+3y[\/latex].<\/p>\n<p>A term without a variable is called a <b>constant <\/b>term, and the degree of that term is\u00a0[latex]0[\/latex]. For example\u00a0[latex]13[\/latex] is the constant term in [latex]3y+13[\/latex]. You would usually say that [latex]14y^{3}+3y[\/latex] has no constant term or that the constant term is\u00a0[latex]0[\/latex].<\/p>\n<p>The following video illustrates how to identify which expressions are polynomials.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-1\" title=\"Determine if an Expression is a Polynomial\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/nPAqfuoSbPI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Evaluate a polynomial<\/h2>\n<p>You can evaluate polynomials just as you can other kinds of expressions. To evaluate an expression for a value of the variable, you 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=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Evaluate [latex]3x^{2}-2x+1[\/latex] for [latex]x=-1[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q280466\">Show Solution<\/span><\/p>\n<div id=\"q280466\" class=\"hidden-answer\" style=\"display: none\">Substitute [latex]-1[\/latex] for each <i>x<\/i> in the polynomial.<\/p>\n<p style=\"text-align: center;\">[latex]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\u00a0[latex]3[\/latex] times\u00a0[latex]1[\/latex], and then multiply [latex]-2[\/latex] times [latex]-1[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]3+\\left(-2\\right)\\left(-1\\right)+1[\/latex]<\/p>\n<p>Change the subtraction to addition of the opposite.<\/p>\n<p style=\"text-align: center;\">[latex]3+2+1[\/latex]<\/p>\n<p>Find the sum.<\/p>\n<h4>Answer<\/h4>\n<p>[latex]3x^{2}-2x+1=6[\/latex], for [latex]x=-1[\/latex]<\/p>\n<\/div>\n<\/div>\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<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q745542\">Show Solution<\/span><\/p>\n<div id=\"q745542\" class=\"hidden-answer\" style=\"display: none\">Substitute\u00a0[latex]3[\/latex] for each <i>p<\/i> in the polynomial.<\/p>\n<p style=\"text-align: center;\">[latex]\\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 and then multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\\displaystyle -\\frac{2}{3}\\left(81\\right)+2\\left(27\\right)-3[\/latex]<\/p>\n<p>Add and then subtract to get [latex]-3[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]-54 + 54 \u2013 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>\n<\/div>\n<p class=\"no-indent\" style=\"text-align: left;\">\u00a0In the following video we show more examples of evaluating polynomials for given values of the variable.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" 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\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-57\">\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 Souse (Mathispower4u.com). <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>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><\/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. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/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>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay, et al.. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at :http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/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":395986,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Evaluate a Polynomial in One Variable\",\"author\":\"James Souse (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/2EeFrgQP1hM\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"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 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