{"id":1348,"date":"2015-11-12T18:35:30","date_gmt":"2015-11-12T18:35:30","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&#038;p=1348"},"modified":"2017-03-31T22:45:59","modified_gmt":"2017-03-31T22:45:59","slug":"introduction-to-dividing-polynomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/chapter\/introduction-to-dividing-polynomials\/","title":{"raw":"Introduction to Dividing Polynomials","rendered":"Introduction to Dividing Polynomials"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>LEARNING OBJECTIVES<\/h3>\r\nBy the end of this lesson, you will be able to:\r\n<ul>\r\n \t<li>Use long division to divide polynomials.<\/li>\r\n \t<li>Use synthetic division to divide polynomials.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<figure id=\"Figure_03_05_001\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"488\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201519\/CNX_Precalc_Figure_03_05_0012.jpg\" alt=\"Lincoln Memorial.\" width=\"488\" height=\"286\" \/> <b>Figure 1.<\/b> Lincoln Memorial, Washington, D.C. (credit: Ron Cogswell, Flickr)[\/caption]<\/figure>\r\n<p id=\"fs-id1165135382145\">The exterior of the Lincoln Memorial in Washington, D.C., is a large rectangular solid with length 61.5 meters (m), width 40 m, and height 30 m.[footnote]National Park Service. \"Lincoln Memorial Building Statistics.\" <a href=\"http:\/\/www.nps.gov\/linc\/historyculture\/lincoln-memorial-building-statistics.htm\" target=\"_blank\">http:\/\/www.nps.gov\/linc\/historyculture\/lincoln-memorial-building-statistics.htm<\/a>. Accessed 4\/3\/2014[\/footnote]\u00a0We can easily find the volume using elementary geometry.<\/p>\r\n\r\n<div id=\"eip-435\" class=\"equation unnumbered\" style=\"text-align: center\">[latex]\\begin{cases}V=l\\cdot w\\cdot h\\hfill \\\\ \\text{ }=61.5\\cdot 40\\cdot 30\\hfill \\\\ \\text{ }=73,800\\hfill \\end{cases}[\/latex]<\/div>\r\n<p id=\"fs-id1165133214948\">So the volume is 73,800 cubic meters [latex]\\left(\\text{m}{^3} \\right).[\/latex]\u00a0Suppose we knew the volume, length, and width. We could divide to find the height.<\/p>\r\n\r\n<div id=\"eip-312\" class=\"equation unnumbered\" style=\"text-align: center\">[latex]\\begin{cases}h=\\frac{V}{l\\cdot w}\\hfill \\\\ \\text{ }=\\frac{73,800}{61.5\\cdot 40}\\hfill \\\\ \\text{ }=30\\hfill \\end{cases}[\/latex]<\/div>\r\n<p id=\"fs-id1165137892463\">As we can confirm from the dimensions above, the height is 30 m. We can use similar methods to find any of the missing dimensions. We can also use the same method if any or all of the measurements contain variable expressions. For example, suppose the volume of a rectangular solid is given by the polynomial [latex]3{x}^{4}-3{x}^{3}-33{x}^{2}+54x.[\/latex]\u00a0The length of the solid is given by 3<em>x<\/em>;\u00a0the width is given by [latex]x - 2.[\/latex]\u00a0To find the height of the solid, we can use polynomial division, which is the focus of this section.<\/p>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>LEARNING OBJECTIVES<\/h3>\n<p>By the end of this lesson, you will be able to:<\/p>\n<ul>\n<li>Use long division to divide polynomials.<\/li>\n<li>Use synthetic division to divide polynomials.<\/li>\n<\/ul>\n<\/div>\n<figure id=\"Figure_03_05_001\">\n<div style=\"width: 498px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/11\/25201519\/CNX_Precalc_Figure_03_05_0012.jpg\" alt=\"Lincoln Memorial.\" width=\"488\" height=\"286\" \/><\/p>\n<p class=\"wp-caption-text\"><b>Figure 1.<\/b> Lincoln Memorial, Washington, D.C. (credit: Ron Cogswell, Flickr)<\/p>\n<\/div>\n<\/figure>\n<p id=\"fs-id1165135382145\">The exterior of the Lincoln Memorial in Washington, D.C., is a large rectangular solid with length 61.5 meters (m), width 40 m, and height 30 m.<a class=\"footnote\" title=\"National Park Service. &quot;Lincoln Memorial Building Statistics.&quot; http:\/\/www.nps.gov\/linc\/historyculture\/lincoln-memorial-building-statistics.htm. Accessed 4\/3\/2014\" id=\"return-footnote-1348-1\" href=\"#footnote-1348-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a>\u00a0We can easily find the volume using elementary geometry.<\/p>\n<div id=\"eip-435\" class=\"equation unnumbered\" style=\"text-align: center\">[latex]\\begin{cases}V=l\\cdot w\\cdot h\\hfill \\\\ \\text{ }=61.5\\cdot 40\\cdot 30\\hfill \\\\ \\text{ }=73,800\\hfill \\end{cases}[\/latex]<\/div>\n<p id=\"fs-id1165133214948\">So the volume is 73,800 cubic meters [latex]\\left(\\text{m}{^3} \\right).[\/latex]\u00a0Suppose we knew the volume, length, and width. We could divide to find the height.<\/p>\n<div id=\"eip-312\" class=\"equation unnumbered\" style=\"text-align: center\">[latex]\\begin{cases}h=\\frac{V}{l\\cdot w}\\hfill \\\\ \\text{ }=\\frac{73,800}{61.5\\cdot 40}\\hfill \\\\ \\text{ }=30\\hfill \\end{cases}[\/latex]<\/div>\n<p id=\"fs-id1165137892463\">As we can confirm from the dimensions above, the height is 30 m. We can use similar methods to find any of the missing dimensions. We can also use the same method if any or all of the measurements contain variable expressions. For example, suppose the volume of a rectangular solid is given by the polynomial [latex]3{x}^{4}-3{x}^{3}-33{x}^{2}+54x.[\/latex]\u00a0The length of the solid is given by 3<em>x<\/em>;\u00a0the width is given by [latex]x - 2.[\/latex]\u00a0To find the height of the solid, we can use polynomial division, which is the focus of this section.<\/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-1348\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Precalculus. <strong>Authored by<\/strong>: Jay Abramson, et al.. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\">http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175<\/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\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section><hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-1348-1\">National Park Service. \"Lincoln Memorial Building Statistics.\" <a href=\"http:\/\/www.nps.gov\/linc\/historyculture\/lincoln-memorial-building-statistics.htm\" target=\"_blank\">http:\/\/www.nps.gov\/linc\/historyculture\/lincoln-memorial-building-statistics.htm<\/a>. Accessed 4\/3\/2014 <a href=\"#return-footnote-1348-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":276,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Precalculus\",\"author\":\"Jay Abramson, et al.\",\"organization\":\"OpenStax\",\"url\":\"http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download For Free at : http:\/\/cnx.org\/contents\/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175.\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1348","chapter","type-chapter","status-publish","hentry"],"part":1346,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1348","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/users\/276"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1348\/revisions"}],"predecessor-version":[{"id":2913,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1348\/revisions\/2913"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/1346"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/1348\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/media?parent=1348"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1348"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/contributor?post=1348"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/odessa-collegealgebra\/wp-json\/wp\/v2\/license?post=1348"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}