{"id":1078,"date":"2018-10-25T16:49:09","date_gmt":"2018-10-25T16:49:09","guid":{"rendered":"http:\/\/lash.utrng.edu.mx\/?p=1078"},"modified":"2018-11-07T20:03:08","modified_gmt":"2018-11-07T20:03:08","slug":"factorizacion-identificando-si-el-trinomio-es-perfecto-o-no","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=1078","title":{"rendered":"Factorizaci\u00f3n identificando si el trinomio es perfecto o no"},"content":{"rendered":"\n<p class=\"has-text-color has-background has-medium-font-size has-very-dark-gray-color has-vivid-green-cyan-background-color\"><strong>Cuando nos encontramos con un trinomio cuadrado perfecto\ufeff<\/strong><\/p>\n\n\n\n<p style=\"text-align:center\" class=\"has-medium-font-size\"><strong>X<\/strong><sup><strong>2<\/strong><\/sup><strong>&nbsp;+ 8x + 16 = 0<\/strong><\/p>\n\n\n\n<p><strong>X<\/strong><sup><strong>2<\/strong><\/sup><strong>&nbsp;+ 8x + 16 = 0<\/strong>&nbsp; Nos damos cuenta de que es un <strong>Trinomio cuadrado perfecto<\/strong>. Sabemos que es perfecto <strong>cuando la ra\u00edz cuadrada del t\u00e9rmino cuadr\u00e1tico<\/strong>(1) y el <strong>t\u00e9rmino Lineal<\/strong>(16) <strong>son<\/strong> n\u00fameros <strong>enteros.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>(x + _____ )(x + _____) = 0<\/strong>&nbsp; Colocamos los par\u00e9ntesis y buscamos los valores que satisfagan la ecuaci\u00f3n, es decir que <strong>multiplicados<\/strong> den&nbsp;<strong>16<\/strong>&nbsp;y <strong>sumados<\/strong> den&nbsp;<strong>8<\/strong>.<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>(x + 4)(x + 4) = 0&nbsp;<\/strong> &nbsp;Factorizando como un binomio al cuadrado aqu\u00ed mostrado en forma de factores<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>x+4=0 | x+4=0<\/strong>&nbsp; &nbsp; Aplicando la propiedad del producto nulo.<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>x<sub>1<\/sub>=\u22124 | x<sub>2<\/sub>=\u22124<\/strong>&nbsp; &nbsp; Despejando.<\/li><\/ul>\n\n\n\n<!--more-->\n\n\n\n<p class=\"has-background has-medium-font-size has-vivid-green-cyan-background-color\"><strong>Cuando nos encontramos con un trinomio cuadrado No perfecto<\/strong><\/p>\n\n\n\n<p style=\"text-align:center\" class=\"has-medium-font-size\"><strong>2x<sup>2&nbsp;<\/sup>+ 7x \u2212 4 = 0<\/strong><\/p>\n\n\n\n<p><strong>2x<sup>2&nbsp;<\/sup>+ 7x \u2212 4 = 0&nbsp; No<\/strong> es un <strong>trinomio cuadrado perfecto<\/strong>, porque la <strong>ra\u00edz cuadrada del t\u00e9rmino cuadr\u00e1tico (2)<\/strong> y el <strong>t\u00e9rmino lineal (7<\/strong>) deben ser n\u00fameros enteros y en este caso no lo son, entonces hay que buscar dos n\u00fameros que <strong>multiplicados<\/strong> den&nbsp;<strong>2<\/strong>&nbsp;y otros dos que <strong>multiplicados<\/strong> den&nbsp;<strong>4<\/strong><br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"200\" height=\"173\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/triNoPerfe-1.png\" alt=\"\" class=\"wp-image-1081\"\/><\/figure><\/div>\n\n\n\n<p>Una vez encontrados los valores que satisfacen el punto anterior, los colocamos de la siguiente manera, para que al multiplicar de forma cruzada y sumar estos valores nos d\u00e9 como resultado el coeficiente del t\u00e9rmino lineal. En este caso para que la <strong>suma<\/strong> d\u00e9 <strong>7<\/strong> debemos agregar un signo menos, pero los signos se agregan en la segunda columna.Solo falta ordenar los t\u00e9rminos encontrados en los par\u00e9ntesis.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/triNoPerfe-2.png\"><img loading=\"lazy\" decoding=\"async\" width=\"316\" height=\"101\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/triNoPerfe-2.png\" alt=\"\" class=\"wp-image-1083\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/triNoPerfe-2.png 316w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/10\/triNoPerfe-2-300x96.png 300w\" sizes=\"auto, (max-width: 316px) 100vw, 316px\" \/><\/a><\/figure><\/div>\n\n\n\n<p>\n\nAntes de proceder a encontrar las soluciones hay que verificar si el producto de los binomios cumple con la ecuaci\u00f3n original. Para ello se multiplica como lo indican las flechas.\n\n<\/p>\n\n\n\n<p style=\"text-align:left\">Ordenando t\u00e9rminos:<\/p>\n\n\n\n<p style=\"text-align:center\" class=\"has-medium-font-size\"><strong>(2x \u2212 1) (x + 4)= 2x<\/strong><sup><strong>2<\/strong><\/sup>\u00a0<strong>+ 7x \u2013 4<\/strong><br><\/p>\n\n\n\n<p>Aplicando la propiedad del producto nulo:<\/p>\n\n\n\n<p style=\"text-align:center\" class=\"has-medium-font-size\"><strong>2x \u2212 1 = 0\u00a0 \u00a0 \u00a0x + 4 = 0<\/strong><br><\/p>\n\n\n\n<p>Despejando:<\/p>\n\n\n\n<p style=\"text-align:center\" class=\"has-medium-font-size\"><strong>x<\/strong><sub><strong>1<\/strong><\/sub><strong>=\u00bd\u00a0\u00a0\u00a0\u00a0x<\/strong><sub><strong>2<\/strong><\/sub><strong>=\u22124<\/strong><\/p>\n\n\n\n<p class=\"has-background has-medium-font-size has-pale-cyan-blue-background-color\"><strong>Ejercicios<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/1-1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"289\" height=\"150\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/1-1.png\" alt=\"\" class=\"wp-image-1138\"\/><\/a><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-gallery columns-2 wp-block-gallery-1 is-layout-flex wp-block-gallery-is-layout-flex\"><li class=\"blocks-gallery-item\"><figure><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/a.png\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"255\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/a.png\" alt=\"\" data-id=\"1140\" data-link=\"http:\/\/lash.utrng.edu.mx\/index.php\/2018\/10\/25\/factorizacion-identificando-si-el-trinomio-es-perfecto-o-no\/a-2\/\" class=\"wp-image-1140\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/a.png 859w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/a-300x89.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/a-768x228.png 768w\" sizes=\"auto, (max-width: 859px) 100vw, 859px\" \/><\/a><\/figure><\/li><li class=\"blocks-gallery-item\"><figure><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/b.png\"><img loading=\"lazy\" decoding=\"async\" width=\"855\" height=\"247\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/b.png\" alt=\"\" data-id=\"1139\" data-link=\"http:\/\/lash.utrng.edu.mx\/index.php\/2018\/10\/25\/factorizacion-identificando-si-el-trinomio-es-perfecto-o-no\/b\/\" class=\"wp-image-1139\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/b.png 855w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/b-300x87.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2018\/11\/b-768x222.png 768w\" sizes=\"auto, (max-width: 855px) 100vw, 855px\" \/><\/a><\/figure><\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Cuando nos encontramos con un trinomio cuadrado perfecto\ufeff X2&nbsp;+ 8x + 16 = 0 X2&nbsp;+ 8x + 16 = 0&nbsp; Nos damos cuenta de que es un Trinomio cuadrado perfecto. Sabemos que es perfecto cuando la ra\u00edz cuadrada del t\u00e9rmino cuadr\u00e1tico(1) y el t\u00e9rmino Lineal(16) son n\u00fameros enteros. (x + _____ )(x + _____) = &hellip; <a href=\"https:\/\/lash.utrng.edu.mx\/?p=1078\">Seguir leyendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[28],"tags":[],"class_list":["post-1078","post","type-post","status-publish","format-standard","hentry","category-primerparcialmate"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/1078","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1078"}],"version-history":[{"count":8,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/1078\/revisions"}],"predecessor-version":[{"id":1141,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/1078\/revisions\/1141"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1078"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1078"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1078"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}