{"id":116347,"date":"2020-01-29T18:22:14","date_gmt":"2020-01-29T17:22:14","guid":{"rendered":"https:\/\/www.superprof.es\/diccionario\/algebra\/teorema-resto.html"},"modified":"2024-05-27T17:40:10","modified_gmt":"2024-05-27T15:40:10","slug":"teorema-resto","status":"publish","type":"post","link":"https:\/\/www.superprof.es\/diccionario\/matematicas\/algebra\/teorema-resto.html","title":{"rendered":"Teorema del resto"},"content":{"rendered":"<section style=\"\">\n<p class=\"\">El <strong>resto de la divisi\u00f3n<\/strong> de un polinomio P(x), entre un polinomio de la forma  (x \u2212 a)  es el <strong>valor num\u00e9rico de dicho polinomio<\/strong> para el valor: x = a.<\/p>\n<p class=\"actividades_v_ir\">P(x) :  Q(x)<\/p>\n<p class=\"\">P(x)= x<sup>4<\/sup> \u2212 3x<sup>2<\/sup> +2           Q(x)= x  \u2212 3  <\/p>\n<h2 class=\"te\">Calculo el resto de la divisi\u00f3n por el teorema del resto<\/h2>\n<p class=\"actividades_2_v\">P(3) = 3<sup>4<\/sup> \u2212 3 \u00b7 3<sup>2<\/sup> + 2 = 81  \u2212 27 + 2 =<span class=\"sol\"> 56 <\/span><\/p>\n<h2 class=\"t\">Ejercicios<\/h2>\n<p class=\"actividades\">Halla el resto de las siguientes divisiones:<\/p>\n<p class=\"actividades\">\n<h2>1<\/h2>\n<p>(x<sup>5<\/sup> \u2212 2x<sup>2<\/sup>  \u2212 3) : (x \u22121)<\/p>\n<p class=\"actividades_2_v_ir\"> R(1) = 1<sup>5<\/sup> \u2212 2 \u00b7 1<sup>2<\/sup> \u2212 3 =  \u22124<\/p>\n<p class=\"actividades\">\n<h2>2<\/h2>\n<p>(2x<sup>4<\/sup> \u2212 2x<sup>3<\/sup> + 3x<sup>2<\/sup> + 5x +10 ) : (x + 2) <\/p>\n<p class=\"actividades_2_v_ir\"> R(\u22122) = 2 \u00b7 (\u22122)<sup>4<\/sup> \u2212 2 \u00b7 (\u22122)<sup>3<\/sup> + 3 \u00b7 (\u22122)<sup>2<\/sup> + 5\u00b7 (\u22122) + 10 =<\/p>\n<p class=\"actividades_2_v_ir\">= 32 + 16 + 12 \u2212 10 + 10 = 60 <\/p>\n<p class=\"actividades\">Indica cu\u00e1les de estas divisiones son exactas:<\/p>\n<p class=\"actividades\">\n<h2>1<\/h2>\n<p>(x<sup>3<\/sup>  \u2212 5x  \u2212 1) : (x  \u2212 3) <\/p>\n<p class=\"actividades_2_v_ir\">P(3) = 3<sup>3<\/sup> \u2212 5 \u00b7 3  \u2212 1 = 27  \u2212 15  \u2212 1 \u2260 0<\/p>\n<p class=\"actividades_2_v_ir\">No es exacta.  <\/p>\n<p class=\"actividades\">\n<h2>2<\/h2>\n<p>(x<sup>6<\/sup> \u2212 1) : (x + 1)  <\/p>\n<p class=\"actividades_2_v_ir\">P(\u22121) = (\u22121)<sup>6<\/sup> \u2212 1 = 0 <\/p>\n<p class=\"actividades_2_v_ir\">Exacta<\/p>\n<p class=\"actividades\">\n<h2>3<\/h2>\n<p>(x<sup>4<\/sup>  \u2212 2x<sup>3<\/sup> + x<sup>2<\/sup> + x  \u2212 1) : (x  \u2212 1) <\/p>\n<p class=\"actividades_2_v_ir\">P(1) = 1<sup>4<\/sup> \u2212 2 \u00b7 1<sup>3<\/sup> + 1 <sup>2<\/sup> + 1  \u2212 1 = 1  \u2212 2 + 1 + 1  \u2212 1 = 0 <\/p>\n<p class=\"actividades_2_v_ir\">Exacta <\/p>\n<p class=\"actividades\">\n<h2>4<\/h2>\n<p>(x<sup>10<\/sup> \u2212 1024) : (x + 2) <\/p>\n<p class=\"actividades_2_v_ir\">P(\u22122) = (\u22122)<sup>10<\/sup> \u2212 1024 =  1024 \u2212 1024 = 0<\/p>\n<p class=\"actividades_2_v_ir\">Exacta <\/p>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>El resto de la divisi\u00f3n de un polinomio P(x), entre un polinomio de la forma (x \u2212 a) es el valor num\u00e9rico de dicho polinomio para el valor: x = a. P(x) : Q(x) P(x)= x4 \u2212 3&#215;2 +2 Q(x)= x \u2212 3 Calculo el resto de la divisi\u00f3n por el teorema del resto P(3) [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","advgb_blocks_editor_width":"","advgb_blocks_columns_visual_guide":"","footnotes":""},"categories":[378],"tags":[364],"class_list":["post-116347","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-t"],"acf":[],"author_meta":{"display_name":"Andra","author_link":"https:\/\/www.superprof.es\/diccionario\/author\/andra"},"featured_img":null,"coauthors":[],"tax_additional":{"categories":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/algebra\" class=\"advgb-post-tax-term\">\u00c1lgebra<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">\u00c1lgebra<\/span>"]},"tags":{"linked":["<a href=\"https:\/\/www.superprof.es\/diccionario\/matematicas\/algebra\" class=\"advgb-post-tax-term\">t<\/a>"],"unlinked":["<span class=\"advgb-post-tax-term\">t<\/span>"]}},"comment_count":"0","relative_dates":{"created":"Publicado 6 a\u00f1os hace","modified":"Actualizado 2 a\u00f1os hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 27 mayo 2024"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 22 min","modified":"Actualizado el 27 mayo 2024 17 h 40 min"},"featured_img_caption":"","series_order":"","_links":{"self":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/116347","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/comments?post=116347"}],"version-history":[{"count":1,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/116347\/revisions"}],"predecessor-version":[{"id":136005,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/116347\/revisions\/136005"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=116347"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=116347"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=116347"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}