{"id":1205,"date":"2016-10-21T20:53:58","date_gmt":"2016-10-21T20:53:58","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakercollegealgebra\/?post_type=chapter&#038;p=1205"},"modified":"2017-08-15T20:51:29","modified_gmt":"2017-08-15T20:51:29","slug":"introduction-polynomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/chapter\/introduction-polynomials\/","title":{"raw":"Introduction to Polynomial Basics","rendered":"Introduction to Polynomial Basics"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Identify the degree and leading coefficient of polynomials.<\/li>\r\n \t<li>Add and subtract polynomials.<\/li>\r\n \t<li>Multiply polynomials.<\/li>\r\n \t<li>Use FOIL to multiply binomials.<\/li>\r\n \t<li>Perform operations with polynomials of several variables.<\/li>\r\n<\/ul>\r\n<\/div>\r\nEarl is building a doghouse, whose front is in the shape of a square topped with a triangle. There will be a rectangular door through which the dog can enter and exit the house. Earl wants to find the area of the front of the doghouse so that he can purchase the correct amount of paint. Using the measurements of the front of the house, shown in Figure 1, we can create an expression that combines several variable terms, allowing us to solve this problem and others like it.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/21205143\/CNX_CAT_Figure_01_04_001.jpg\" alt=\"Sketch of a house formed by a square and a triangle based on the top of the square. A rectangle is placed at the bottom center of the square to mark a doorway. The height of the door is labeled: x and the width of the door is labeled: 1 foot. The side of the square is labeled: 2x. The height of the triangle is labeled: 3\/2 feet.\" width=\"487\" height=\"249\" data-media-type=\"image\/jpg\" \/> <b>Figure 1<\/b>[\/caption]\r\n\r\nFirst find the area of the square in square feet.\r\n<div style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill A&amp; =&amp; {s}^{2}\\hfill \\\\ &amp; =&amp; {\\left(2x\\right)}^{2}\\hfill \\\\ &amp; =&amp; 4{x}^{2}\\hfill \\end{array}[\/latex]<\/div>\r\nThen find the area of the triangle in square feet.\r\n<div style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill A&amp; =&amp; \\frac{1}{2}bh\\hfill \\\\ &amp; =&amp; \\text{ }\\frac{1}{2}\\left(2x\\right)\\left(\\frac{3}{2}\\right)\\hfill \\\\ &amp; =&amp; \\text{ }\\frac{3}{2}x\\hfill \\end{array}[\/latex]<\/div>\r\nNext find the area of the rectangular door in square feet.\r\n<div style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill A&amp; =&amp; lw\\hfill \\\\ &amp; =&amp; x\\cdot 1\\hfill \\\\ \\hfill &amp; =&amp; x\\hfill \\end{array}[\/latex]<\/div>\r\nThe area of the front of the doghouse can be found by adding the areas of the square and the triangle, and then subtracting the area of the rectangle. When we do this, we get [latex]4{x}^{2}+\\frac{3}{2}x-x{\\text{ft}}^{2}[\/latex], or [latex]4{x}^{2}+\\frac{1}{2}x[\/latex] ft<sup>2<\/sup>.\r\n\r\nIn this section, we will examine expressions such as this one, which combine several variable terms.","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Identify the degree and leading coefficient of polynomials.<\/li>\n<li>Add and subtract polynomials.<\/li>\n<li>Multiply polynomials.<\/li>\n<li>Use FOIL to multiply binomials.<\/li>\n<li>Perform operations with polynomials of several variables.<\/li>\n<\/ul>\n<\/div>\n<p>Earl is building a doghouse, whose front is in the shape of a square topped with a triangle. There will be a rectangular door through which the dog can enter and exit the house. Earl wants to find the area of the front of the doghouse so that he can purchase the correct amount of paint. Using the measurements of the front of the house, shown in Figure 1, we can create an expression that combines several variable terms, allowing us to solve this problem and others like it.<\/p>\n<div style=\"width: 497px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/10\/21205143\/CNX_CAT_Figure_01_04_001.jpg\" alt=\"Sketch of a house formed by a square and a triangle based on the top of the square. A rectangle is placed at the bottom center of the square to mark a doorway. The height of the door is labeled: x and the width of the door is labeled: 1 foot. The side of the square is labeled: 2x. The height of the triangle is labeled: 3\/2 feet.\" width=\"487\" height=\"249\" data-media-type=\"image\/jpg\" \/><\/p>\n<p class=\"wp-caption-text\"><b>Figure 1<\/b><\/p>\n<\/div>\n<p>First find the area of the square in square feet.<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill A& =& {s}^{2}\\hfill \\\\ & =& {\\left(2x\\right)}^{2}\\hfill \\\\ & =& 4{x}^{2}\\hfill \\end{array}[\/latex]<\/div>\n<p>Then find the area of the triangle in square feet.<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill A& =& \\frac{1}{2}bh\\hfill \\\\ & =& \\text{ }\\frac{1}{2}\\left(2x\\right)\\left(\\frac{3}{2}\\right)\\hfill \\\\ & =& \\text{ }\\frac{3}{2}x\\hfill \\end{array}[\/latex]<\/div>\n<p>Next find the area of the rectangular door in square feet.<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\hfill A& =& lw\\hfill \\\\ & =& x\\cdot 1\\hfill \\\\ \\hfill & =& x\\hfill \\end{array}[\/latex]<\/div>\n<p>The area of the front of the doghouse can be found by adding the areas of the square and the triangle, and then subtracting the area of the rectangle. When we do this, we get [latex]4{x}^{2}+\\frac{3}{2}x-x{\\text{ft}}^{2}[\/latex], or [latex]4{x}^{2}+\\frac{1}{2}x[\/latex] ft<sup>2<\/sup>.<\/p>\n<p>In this section, we will examine expressions such as this one, which combine several variable terms.<\/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-1205\">\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>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>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/a>. <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\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: OpenStax College Algebra. <strong>Provided by<\/strong>: OpenStax. <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\/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":21,"menu_order":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"College Algebra\",\"author\":\"OpenStax College Algebra\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\",\"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\":\"College Algebra\",\"author\":\"Abramson, Jay et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@5.2\"}]","CANDELA_OUTCOMES_GUID":"6c21176e-df09-4046-8cb2-7420344c36e1","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1205","chapter","type-chapter","status-publish","hentry"],"part":1203,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1205","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1205\/revisions"}],"predecessor-version":[{"id":4399,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1205\/revisions\/4399"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1203"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1205\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/media?parent=1205"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1205"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1205"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/license?post=1205"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}