El polinomio P(x) es divisible por un polinomio de la forma (x - a) si y s\u00f3lo si P(x = a) = 0.<\/p>\n

Al valor x = a<\/strong> se le llama ra\u00edz<\/strong><\/span> o cero<\/strong><\/span> de P(x).<\/p>\n

Las ra\u00edces o ceros de un polinomio<\/strong> son los valores<\/strong> que anulan el polinomio<\/strong>.<\/p>\n

Ejercicio<\/h2>\n
Comprueba que los siguientes polinomios tienen como factores los que se indican: <\/p>\n
\n
1<\/h2>\n
(x^{3<\/sup> \u2212 5x \u2212 1) tiene por factor (x \u2212 3) <\/p>\n}
(x^{3<\/sup> \u2212 5x \u22121) es divisible por (x \u2212 3) si y s\u00f3lo si P(x = 3) = 0. <\/p>\n}
P(3) = 3^{3<\/sup> \u2212 5 \u00b7 3 \u2212 1 = 27 \u2212 15 \u2212 1 \u2260 0<\/p>\n}
(x \u2212 3) no es un factor. <\/p>\n
\n
2<\/h2>\n
(x^{6<\/sup> \u2212 1) tiene por factor (x + 1) <\/p>\n}
(x^{6<\/sup> \u2212 1) es divisible por (x + 1) si y s\u00f3lo si P(x = \u2212 1) = 0. <\/p>\n}
P(\u22121) = (\u22121)^{6<\/sup> \u2212 1 = 0 <\/p>\n}
(x + 1) es un factor. <\/p>\n
\n
3<\/h2>\n
(x^{4<\/sup> \u2212 2x^{3<\/sup> + x^{2<\/sup> + x \u2212 1) tiene por factor (x \u2212 1) <\/p>\n}}}
(x^{4<\/sup> \u2212 2x^{3<\/sup> + x^{2<\/sup> + x \u2212 1) es divisible por (x \u2212 1 ) si y s\u00f3lo si P(x = 1) = 0. <\/p>\n}}}
P(1) = 1^{4<\/sup> \u2212 2 \u00b7 1^{3<\/sup> + 1 ^{2<\/sup> + 1 \u2212 1 = 1 \u2212 2 + 1 + 1 \u2212 1 = 0 <\/p>\n}}}
(x \u2212 1) es un factor. <\/p>\n
\n
4<\/h2>\n
(x^{10<\/sup> \u2212 1024) tiene por factor (x + 2) <\/p>\n}
(x^{10<\/sup> \u2212 1024) es divisible por (x + 2) si y s\u00f3lo si P(x = \u2212 2) = 0. <\/p>\n}
P(\u22122) = (\u22122)^{10<\/sup> \u2212 1024 = 1024 \u2212 1024 = 0<\/p>\n}
(x + 2) es un factor. <\/p>\n
Calculo las ra\u00edces del polinomio:<\/h2>\n
Q(x) = x^{2<\/sup> \u2212 x \u2212 6 <\/p>\n}
Los divisores del t\u00e9rmino independiente son \u00b11, \u00b12, \u00b13.<\/p>\n
Q(1) = 1^{2<\/sup> \u2212 1 \u2212 6 \u2260 0<\/p>\n}
Q(\u22121) = (\u22121)^{2<\/sup> \u2212 (\u22121) \u2212 6 \u2260 0 <\/p>\n}
Q(2) = 2^{2<\/sup> \u2212 2 \u2212 6 \u2260 0<\/p>\n}
Q(\u22122) = (\u22122)^{2<\/sup> \u2212 (\u22122) \u2212 6 = 4 +2 +6 = 0<\/p>\n}
Q(3) = 3^{2<\/sup> \u2212 3 \u2212 6 = 9 \u2212 3 \u2212 6 = 0 <\/p>\n}
x = \u22122 y x = 3 son las ra\u00edces o ceros del polinomio<\/strong>: P(x) = x^{2<\/sup> \u2212 x \u2212 6, porque P(\u22122) = 0 y P(3) = 0.<\/strong> <\/p>\n}
P(x) = (x + 2) \u00b7 (x \u2212 3)<\/strong><\/p>\n<\/section>\n","protected":false},"excerpt":{"rendered":"
El polinomio P(x) es divisible por un polinomio de la forma (x – a) si y s\u00f3lo si P(x = a) = 0. Al valor x = a se le llama ra\u00edz o cero de P(x). Las ra\u00edces o ceros de un polinomio son los valores que anulan el polinomio. Ejercicio Comprueba que los siguientes […]<\/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-116346","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":["\u00c1lgebra<\/a>"],"unlinked":["\u00c1lgebra<\/span>"]},"tags":{"linked":["t<\/a>"],"unlinked":["t<\/span>"]}},"comment_count":"0","relative_dates":{"created":"Publicado 6 a\u00f1os hace","modified":"Actualizado 6 a\u00f1os hace"},"absolute_dates":{"created":"Publicado el 29 enero 2020","modified":"Actualizado el 29 enero 2020"},"absolute_dates_time":{"created":"Publicado el 29 enero 2020 18 h 22 min","modified":"Actualizado el 29 enero 2020 18 h 22 min"},"featured_img_caption":"","series_order":"","_links":{"self":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/116346","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=116346"}],"version-history":[{"count":0,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/posts\/116346\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/media?parent=116346"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/categories?post=116346"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.superprof.es\/diccionario\/wp-json\/wp\/v2\/tags?post=116346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

1<\/h2>\n(x3<\/sup> \u2212 5x \u2212 1) tiene por factor (x \u2212 3) <\/p>\n (x3<\/sup> \u2212 5x \u22121) es divisible por (x \u2212 3) si y s\u00f3lo si P(x = 3) = 0. <\/p>\nP(3) = 33<\/sup> \u2212 5 \u00b7 3 \u2212 1 = 27 \u2212 15 \u2212 1 \u2260 0<\/p>\n(x \u2212 3) no es un factor. <\/p>\n\n