{"id":5843,"date":"2024-11-22T11:09:45","date_gmt":"2024-11-22T17:09:45","guid":{"rendered":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/?page_id=5843"},"modified":"2024-11-22T12:48:01","modified_gmt":"2024-11-22T18:48:01","slug":"mn0e","status":"publish","type":"page","link":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/mn\/antecedentes\/mn0e\/","title":{"rendered":"mn0e Polinomios"},"content":{"rendered":"\n<h2>Teorema fundamental del&nbsp;\u00e1lgebra<\/h2>\n\n\n\n<ul>\n<li>Toda ecuaci\u00f3n polinomial de grado n &gt;= 1 tiene al menos una ra\u00edz, real o imaginaria.<\/li>\n\n\n\n<li>Toda ecuaci\u00f3n polinomial f(x) = 0 de grado n tiene exactamente n ra\u00edces. Las ra\u00edces pueden ser reales, reales repetidas y complejas.<\/li>\n\n\n\n<li>Todo polinomio f(x) de grado n &gt;= 1 se puede expresar como el producto de n factores lineales.<\/li>\n\n\n\n<li>Si un n\u00famero complejo a + bi es una ra\u00edz de la ecuaci\u00f3n polinomial con coeficientes reales y con b distinto de cero, entonces su complejo conjugado a \u2013 bi tambi\u00e9n es una ra\u00edz.<\/li>\n<\/ul>\n\n\n\n<p>Esto se muestra con los siguientes polinomios:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa1.jpg?w=459\" alt=\"\" class=\"wp-image-641\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc1.jpg?w=791\" alt=\"\" class=\"wp-image-642\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa2.jpg?w=490\" alt=\"\" class=\"wp-image-643\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc2.jpg?w=777\" alt=\"\" class=\"wp-image-644\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa3.jpg?w=474\" alt=\"\" class=\"wp-image-645\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc3-1.jpg?w=811\" alt=\"\" class=\"wp-image-664\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa4.jpg?w=455\" alt=\"\" class=\"wp-image-647\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc4.jpg?w=772\" alt=\"\" class=\"wp-image-648\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa5.jpg?w=612\" alt=\"\" class=\"wp-image-649\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc5.jpg?w=789\" alt=\"\" class=\"wp-image-651\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa6.jpg?w=646\" alt=\"\" class=\"wp-image-652\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc6.jpg?w=789\" alt=\"\" class=\"wp-image-653\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa7.jpg?w=443\" alt=\"\" class=\"wp-image-655\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc7.jpg?w=799\" alt=\"\" class=\"wp-image-657\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa8.jpg?w=668\" alt=\"\" class=\"wp-image-658\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc8.jpg?w=665\" alt=\"\" class=\"wp-image-656\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa9.jpg?w=675\" alt=\"\" class=\"wp-image-659\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc9-1.jpg?w=792\" alt=\"\" class=\"wp-image-666\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfa10.jpg?w=731\" alt=\"\" class=\"wp-image-661\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/minumero.files.wordpress.com\/2020\/06\/tfc10.jpg?w=804\" alt=\"\" class=\"wp-image-662\" \/><\/figure>\n\n\n\n<h2><strong>Operaciones con polinomios<\/strong><\/h2>\n\n\n\n<h2 class=\"has-text-align-center has-white-background-color has-text-color has-background\" style=\"color:#e80f2c\"><strong>Producto de polinomios<\/strong><\/h2>\n\n\n\n<p>Para multiplicar dos polinomios, se multiplica cada uno de los t\u00e9rminos de un polinomio por los t\u00e9rminos del otro polinomio y se suman los productos parciales.<\/p>\n\n\n\n<p>Para facilitar la operaci\u00f3n, conviene en la mayor\u00eda de los casos, hacer el producto observando lo siguiente.<\/p>\n\n\n\n<ol>\n<li>Ordenar el multiplicando y el multiplicador en el mismo sentido de una letra de mayor a menor grado.<\/li>\n\n\n\n<li>Escribir el producto parcial debajo de cada t\u00e9rmino.<\/li>\n\n\n\n<li>Escribir en una misma l\u00ednea e identificar t\u00e9rminos semejantes.<\/li>\n\n\n\n<li>Efectuar la reducci\u00f3n de t\u00e9rminos semejantes.<\/li>\n<\/ol>\n\n\n\n<p><strong>Ejemplo<\/strong>. Multiplicar los polinomios<\/p>\n\n\n\n<p class=\"has-text-align-center\"><em>a<sup>3<\/sup>&nbsp;+ 4a + 2a<sup>2<\/sup>&nbsp;+ 6<\/em> con <em>a<sup>2<\/sup>&nbsp;+ 3 + 7a<\/em><\/p>\n\n\n\n<p>Ordenando por t\u00e9rminos en relaci\u00f3n a la variable <em>a<\/em>.<\/p>\n\n\n\n<p class=\"has-text-align-center\"><em>a<sup>3<\/sup>&nbsp;+ 2a<sup>2<\/sup>&nbsp;+ 4a + 6<\/em> con  <em>a<sup>2<\/sup>&nbsp;+ 7a + 3<\/em><\/p>\n\n\n\n<p>Resolver productos t\u00e9rmino a t\u00e9rmino<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2023\/08\/imagen-94.png\" alt=\"\" class=\"wp-image-5851\" width=\"305\" height=\"130\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2023\/08\/imagen-94.png 508w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2023\/08\/imagen-94-300x128.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/figure><\/div>\n\n\n<p>Realizar las siguientes multiplicaciones:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2023\/08\/imagen-95.png\" alt=\"\" class=\"wp-image-5852\" width=\"428\" height=\"257\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2023\/08\/imagen-95.png 608w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2023\/08\/imagen-95-300x180.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/figure><\/div>\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2023\/08\/imagen-96.png\" alt=\"\" class=\"wp-image-5853\" width=\"553\" height=\"283\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2023\/08\/imagen-96.png 755w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2023\/08\/imagen-96-300x154.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h2 class=\"has-text-align-center has-text-color\" style=\"color:#ea0826\"><strong>Divisi\u00f3n<\/strong>&nbsp;de un&nbsp;<strong>polinomio<\/strong>&nbsp;por un monomio<\/h2>\n\n\n\n<p>Para esta divisi\u00f3n se divide cada uno de los t\u00e9rminos del polinomio entre el monomio.<\/p>\n\n\n\n<p>Ejemplo. Dividir 32x<sup>4<\/sup>y<sup>3<\/sup>&nbsp;\u2013 40x<sup>2<\/sup>y<sup>4<\/sup>&nbsp;+ 36x<sup>3<\/sup>y<sup>3<\/sup>&nbsp;por \u2013 4x<sup>2<\/sup>y<sup>2<\/sup><\/p>\n\n\n\n<p>32x<sup>4<\/sup>y<sup>3<\/sup>\/ \u2013 4x<sup>2<\/sup>y<sup>2<\/sup>\u00a0= \u2013 8x<sup>2<\/sup>y<\/p>\n\n\n\n<p>\u2013 40x<sup>2<\/sup>y<sup>4<\/sup>\/ \u2013 4x<sup>2<\/sup>y<sup>2<\/sup>&nbsp;= 10y<sup>2<\/sup><\/p>\n\n\n\n<p>36x<sup>3<\/sup>y<sup>3<\/sup>\/ \u2013 4x<sup>2<\/sup>y<sup>2<\/sup>&nbsp;= \u2013 9xy<\/p>\n\n\n\n<p>El resultado es: -8x<sup>2<\/sup>y + 10y<sup>2<\/sup>\u2013 9xy<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2024\/11\/imagen-17.png\" alt=\"\" class=\"wp-image-6633\" width=\"354\" height=\"229\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2024\/11\/imagen-17.png 425w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2024\/11\/imagen-17-300x194.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/figure><\/div>","protected":false},"excerpt":{"rendered":"<p>Teorema fundamental del&nbsp;\u00e1lgebra Esto se muestra con los siguientes polinomios: Operaciones con polinomios Producto de polinomios Para multiplicar dos polinomios, se multiplica cada uno de los t\u00e9rminos de un polinomio por los t\u00e9rminos del otro polinomio y se suman los productos parciales. Para facilitar la operaci\u00f3n, conviene en la mayor\u00eda de los casos, hacer el &hellip; <a href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/mn\/antecedentes\/mn0e\/\" class=\"more-link\">Contin\u00faa leyendo <span class=\"screen-reader-text\">mn0e Polinomios<\/span><\/a><\/p>\n","protected":false},"author":123458,"featured_media":0,"parent":4236,"menu_order":5,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0},"_links":{"self":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5843"}],"collection":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/users\/123458"}],"replies":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/comments?post=5843"}],"version-history":[{"count":5,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5843\/revisions"}],"predecessor-version":[{"id":6634,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/5843\/revisions\/6634"}],"up":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/4236"}],"wp:attachment":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/media?parent=5843"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}