{"id":1304,"date":"2025-10-08T21:15:30","date_gmt":"2025-10-09T03:15:30","guid":{"rendered":"https:\/\/portal.pronea.gt\/?p=1304"},"modified":"2025-10-08T21:15:41","modified_gmt":"2025-10-09T03:15:41","slug":"temporary-title-790-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2","status":"publish","type":"post","link":"https:\/\/portal.pronea.gt\/?p=1304","title":{"rendered":"Ecuaciones polinomiales y funciones racionales"},"content":{"rendered":"<div id=\"cmsmasters_row_\" class=\"cmsmasters_row cmsmasters_color_scheme_default cmsmasters_row_top_default cmsmasters_row_bot_default cmsmasters_row_boxed\">\n<div class=\"cmsmasters_row_outer_parent\">\n<div class=\"cmsmasters_row_outer\">\n<div class=\"cmsmasters_row_inner\">\n<div class=\"cmsmasters_row_margin\">\n<div id=\"cmsmasters_column_\" class=\"cmsmasters_column one_first\">\n<div class=\"cmsmasters_column_inner\"><div class=\"cmsmasters_text\" data-animation=\"fadeIn\">\n<h1 data-start=\"2429\" data-end=\"2479\">Ecuaciones polinomiales y funciones racionales<\/h1>\n<p data-start=\"2481\" data-end=\"2748\">Las <strong data-start=\"2485\" data-end=\"2512\">ecuaciones polinomiales<\/strong> y las <strong data-start=\"2519\" data-end=\"2543\">funciones racionales<\/strong> son parte esencial del lenguaje algebraico. A trav\u00e9s de ellas, podemos representar y resolver problemas donde las variables y sus potencias interact\u00faan para mostrar c\u00f3mo cambia un valor respecto a otro.<\/p>\n<p data-start=\"2750\" data-end=\"2873\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f3a5.svg\" alt=\"\ud83c\udfa5\" \/> <strong data-start=\"2753\" data-end=\"2787\">Mira aqu\u00ed el video del tema<\/strong><\/p>\n<iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/VLt0cvGgZuk?si=Vo-iVOmQFuCk6s_Z\" width=\"1120\" height=\"630\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<hr data-start=\"2875\" data-end=\"2878\" \/>\n<h2 data-start=\"2880\" data-end=\"2920\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f522.svg\" alt=\"\ud83d\udd22\" \/> \u00bfQu\u00e9 es una ecuaci\u00f3n polinomial?<\/h2>\n<p data-start=\"2921\" data-end=\"3031\">Una <strong data-start=\"2925\" data-end=\"2948\">ecuaci\u00f3n polinomial<\/strong> es una igualdad que contiene una o m\u00e1s potencias de una variable.<br data-start=\"3014\" data-end=\"3017\" \/>Por ejemplo:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1307\" src=\"https:\/\/portal.pronea.gt\/wp-content\/uploads\/2025\/10\/funcion_racional1.png\" alt=\"imagen de una ecuaci\u00f3n\" width=\"231\" height=\"60\" \/><\/p>\n<p data-start=\"3057\" data-end=\"3143\">Resolverla significa encontrar los valores de <strong data-start=\"3103\" data-end=\"3108\">x<\/strong> que hacen verdadera la igualdad.<\/p>\n<p data-start=\"3145\" data-end=\"3172\">Existen distintos grados:<\/p>\n<ul>\n<li data-start=\"3175\" data-end=\"3199\"><strong data-start=\"3175\" data-end=\"3187\">Lineales<\/strong> (grado 1)<\/li>\n<li data-start=\"3202\" data-end=\"3229\"><strong data-start=\"3202\" data-end=\"3217\">Cuadr\u00e1ticas<\/strong> (grado 2)<\/li>\n<li data-start=\"3232\" data-end=\"3263\"><strong data-start=\"3232\" data-end=\"3243\">C\u00fabicas<\/strong> (grado 3), y m\u00e1s.<\/li>\n<\/ul>\n<hr data-start=\"3265\" data-end=\"3268\" \/>\n<h2 data-start=\"3270\" data-end=\"3309\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f9e9.svg\" alt=\"\ud83e\udde9\" \/> \u00bfY qu\u00e9 es una funci\u00f3n racional?<\/h2>\n<p data-start=\"3310\" data-end=\"3419\">Una <strong data-start=\"3314\" data-end=\"3334\">funci\u00f3n racional<\/strong> es una fracci\u00f3n donde el numerador y el denominador son polinomios.<br data-start=\"3402\" data-end=\"3405\" \/>Por ejemplo:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist-s\">\u200b<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1308\" src=\"https:\/\/portal.pronea.gt\/wp-content\/uploads\/2025\/10\/funcion_racional.png\" alt=\"Imagen de una funci\u00f3n racional\" width=\"181\" height=\"86\" \/><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"3457\" data-end=\"3611\">Estas funciones tienen comportamientos interesantes, como <strong data-start=\"3515\" data-end=\"3528\">as\u00edntotas<\/strong> y <strong data-start=\"3531\" data-end=\"3548\">restricciones<\/strong>, que podemos analizar al graficarlas en el plano cartesiano.<\/p>\n<hr data-start=\"3613\" data-end=\"3616\" \/>\n<h2 data-start=\"3618\" data-end=\"3651\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4c8.svg\" alt=\"\ud83d\udcc8\" \/> \u00bfPor qu\u00e9 son importantes?<\/h2>\n<p data-start=\"3652\" data-end=\"3732\">Tanto las ecuaciones polinomiales como las funciones racionales se aplican en:<\/p>\n<ul>\n<li data-start=\"3735\" data-end=\"3760\">C\u00e1lculos financieros <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4b0.svg\" alt=\"\ud83d\udcb0\" \/><\/li>\n<li data-start=\"3763\" data-end=\"3790\">An\u00e1lisis de movimiento <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2699.svg\" alt=\"\u2699\ufe0f\" \/><\/li>\n<li data-start=\"3793\" data-end=\"3818\">Modelos estad\u00edsticos <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f4ca.svg\" alt=\"\ud83d\udcca\" \/><\/li>\n<li data-start=\"3821\" data-end=\"3863\">Representaci\u00f3n de fen\u00f3menos naturales <img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f33f.svg\" alt=\"\ud83c\udf3f\" \/><\/li>\n<\/ul>\n<p data-start=\"3865\" data-end=\"3950\">Comprenderlas permite tomar decisiones informadas y razonar con l\u00f3gica y precisi\u00f3n.<\/p>\n<hr data-start=\"3952\" data-end=\"3955\" \/>\n<h2 data-start=\"3957\" data-end=\"3984\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f9e0.svg\" alt=\"\ud83e\udde0\" \/> Aprender con PRONEA<\/h2>\n<p data-start=\"3985\" data-end=\"4309\">El <strong data-start=\"3988\" data-end=\"4043\">Programa Nacional de Educaci\u00f3n Alternativa \u2013PRONEA\u2013<\/strong> del Ministerio de Educaci\u00f3n de Guatemala promueve el aprendizaje aut\u00f3nomo, flexible y adaptado al ritmo de cada estudiante adulto.<br data-start=\"4174\" data-end=\"4177\" \/>A trav\u00e9s de videos, gu\u00edas y actividades, podr\u00e1s dominar temas como <strong data-start=\"4244\" data-end=\"4294\">ecuaciones polinomiales y funciones racionales<\/strong> paso a paso.<\/p>\n<hr data-start=\"4311\" data-end=\"4314\" \/>\n<h2 data-start=\"4316\" data-end=\"4333\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/2705.svg\" alt=\"\u2705\" \/> Conclusi\u00f3n<\/h2>\n<p data-start=\"4334\" data-end=\"4564\">Las matem\u00e1ticas son una herramienta poderosa para entender y transformar el mundo.<br data-start=\"4416\" data-end=\"4419\" \/>Al dominar las <strong data-start=\"4434\" data-end=\"4484\">ecuaciones polinomiales y funciones racionales<\/strong>, estar\u00e1s desarrollando una forma de pensar m\u00e1s anal\u00edtica, precisa y creativa.<\/p>\n<p data-start=\"4566\" data-end=\"4665\"><img decoding=\"async\" class=\"emoji\" role=\"img\" draggable=\"false\" src=\"https:\/\/s.w.org\/images\/core\/emoji\/16.0.1\/svg\/1f449.svg\" alt=\"\ud83d\udc49\" \/> Con el <strong data-start=\"4576\" data-end=\"4586\">PRONEA<\/strong>, cada video es una oportunidad para crecer, aprender y aplicar lo que sabes.<\/p>\n<\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":2,"featured_media":1306,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"_price":"","_stock":"","_tribe_ticket_header":"","_tribe_default_ticket_provider":"","_tribe_ticket_capacity":"0","_ticket_start_date":"","_ticket_end_date":"","_tribe_ticket_show_description":"","_tribe_ticket_show_not_going":false,"_tribe_ticket_use_global_stock":"","_tribe_ticket_global_stock_level":"","_global_stock_mode":"","_global_stock_cap":"","_tribe_rsvp_for_event":"","_tribe_ticket_going_count":"","_tribe_ticket_not_going_count":"","_tribe_tickets_list":"[]","_tribe_ticket_has_attendee_info_fields":false,"footnotes":""},"categories":[33,39],"tags":[],"class_list":["post-1304","post","type-post","status-publish","format-image","has-post-thumbnail","hentry","category-matematicas","category-recursos","post_format-post-format-image"],"_links":{"self":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1304","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1304"}],"version-history":[{"count":3,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1304\/revisions"}],"predecessor-version":[{"id":1310,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/posts\/1304\/revisions\/1310"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=\/wp\/v2\/media\/1306"}],"wp:attachment":[{"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/portal.pronea.gt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}