{"id":830,"date":"2024-04-29T21:49:11","date_gmt":"2024-04-29T21:49:11","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=830"},"modified":"2026-02-02T16:29:35","modified_gmt":"2026-02-02T16:29:35","slug":"polynomial-basics-apply-it-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/polynomial-basics-apply-it-1\/","title":{"raw":"Polynomial Basics: Apply It 1","rendered":"Polynomial Basics: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Recognize polynomial functions, noting their degree and leading coefficient<\/li>\r\n \t<li>Add, subtract, and multiply polynomials using different methods, including the FOIL method for two-term polynomials<\/li>\r\n \t<li>Work with polynomials that have more than one variable, understanding how to combine and simplify them<\/li>\r\n<\/ul>\r\n<\/section>A woodcraft artisan\u2019s most popular items are her pairs of cedar nesting boxes. Her craftsmanship is so precise that one open-topped box fits perfectly inside another. The outer box is a cube with side length [latex]x[\/latex] cm. The box that nests inside of it is a rectangular prism with its open face lying flush with the open face of the outer box. Both boxes, including their bottoms, are made with cedar that is [latex]1[\/latex] cm thick. The outer box (left) and the inner box (right) are depicted below.\r\n\r\n<center>\r\n\r\n[caption id=\"attachment_4203\" align=\"alignnone\" width=\"750\"]<img class=\"wp-image-4203\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes-300x143.jpg\" alt=\"Two open topped boxes (crates), one with all sides labeled x, the other with sides labeled x-1, x-2, and x-2.\" width=\"750\" height=\"358\" \/> Two open boxes with dimensions in terms of\u202f*x*, illustrating how changes in side lengths affect volume.[\/caption]\r\n\r\n<\/center>To help her customize her nesting boxes to her patrons\u2019 volume needs, the artisan uses polynomial expressions to represent the various volumes involved.\r\n\r\n<section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25373[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25374[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25375[\/ohm2_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]25376[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Recognize polynomial functions, noting their degree and leading coefficient<\/li>\n<li>Add, subtract, and multiply polynomials using different methods, including the FOIL method for two-term polynomials<\/li>\n<li>Work with polynomials that have more than one variable, understanding how to combine and simplify them<\/li>\n<\/ul>\n<\/section>\n<p>A woodcraft artisan\u2019s most popular items are her pairs of cedar nesting boxes. Her craftsmanship is so precise that one open-topped box fits perfectly inside another. The outer box is a cube with side length [latex]x[\/latex] cm. The box that nests inside of it is a rectangular prism with its open face lying flush with the open face of the outer box. Both boxes, including their bottoms, are made with cedar that is [latex]1[\/latex] cm thick. The outer box (left) and the inner box (right) are depicted below.<\/p>\n<div style=\"text-align: center;\">\n<figure id=\"attachment_4203\" aria-describedby=\"caption-attachment-4203\" style=\"width: 750px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-4203\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes-300x143.jpg\" alt=\"Two open topped boxes (crates), one with all sides labeled x, the other with sides labeled x-1, x-2, and x-2.\" width=\"750\" height=\"358\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes-300x143.jpg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes-1024x488.jpg 1024w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes-768x366.jpg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes-1536x732.jpg 1536w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes-65x31.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes-225x107.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes-350x167.jpg 350w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/42\/2024\/04\/25052639\/open_topped_boxes.jpg 1600w\" sizes=\"(max-width: 750px) 100vw, 750px\" \/><figcaption id=\"caption-attachment-4203\" class=\"wp-caption-text\">Two open boxes with dimensions in terms of\u202f*x*, illustrating how changes in side lengths affect volume.<\/figcaption><\/figure>\n<\/div>\n<p>To help her customize her nesting boxes to her patrons\u2019 volume needs, the artisan uses polynomial expressions to represent the various volumes involved.<\/p>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm25373\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=25373&theme=lumen&iframe_resize_id=ohm25373&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm25374\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=25374&theme=lumen&iframe_resize_id=ohm25374&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm25375\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=25375&theme=lumen&iframe_resize_id=ohm25375&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try 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