{"id":291,"date":"2023-07-06T18:20:29","date_gmt":"2023-07-06T18:20:29","guid":{"rendered":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/"},"modified":"2023-07-06T18:20:29","modified_gmt":"2023-07-06T18:20:29","slug":"contoh-polinomial-homogen","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/","title":{"rendered":"Polinomial homogen"},"content":{"rendered":"<p>Halaman ini menjelaskan apa itu polinomial homogen. Anda juga akan melihat contoh polinomial homogen dan sifat-sifat polinomial jenis ini. Selain itu, Anda juga akan menemukan perbedaan antara polinomial homogen dan polinomial heterogen. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-polinomio-homogeneo\"><\/span> Apa yang dimaksud dengan polinomial homogen?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Pengertian polinomial homogen adalah sebagai berikut:<\/p>\n<p> <strong>Dalam matematika, polinomial homogen adalah polinomial yang semua sukunya mempunyai derajat yang sama.<\/strong><\/p>\n<p> Contoh polinomial homogen adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c562859bfcb9245bf750cdf62e30cc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y,z)=x^3+5x^2y-4xyz\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"230\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dalam hal ini, ini adalah polinomial homogen derajat 3, karena semua monomial yang merupakan bagian dari polinomial tersebut adalah derajat ketiga.<\/p>\n<p> Jika Anda ragu tentang cara menghitung derajat suatu suku polinomial homogen, Anda dapat melihat halaman kami tentang <a href=\"https:\/\/mathority.org\/id\/bagian-dari-koefisien-monomial,-bagian-literal-dan-derajat-variabel\/\"><strong><span style=\"text-decoration: underline;\">apa saja bagian-bagian dari monomial<\/span><\/strong><\/a> , di mana Anda tidak hanya akan menemukan cara mencari derajat monomial, tetapi juga penjelasan seluruh bagian monomial dan cara mengidentifikasinya. Selain itu, Anda akan dapat melihat contoh dan latihan dengan latihan yang diselesaikan langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-polinomios-homogeneos\"><\/span> Contoh polinomial homogen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita melihat apa yang dimaksud dengan polinomial homogen, mari kita lihat beberapa contoh polinomial homogen untuk menyelesaikan pemahaman konsepnya:<\/p>\n<ul>\n<li> Contoh polinomial homogen derajat 5:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-938803398f7974d4ff410dfb1e43f84e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y)=x^5+3x^2y^3-6x^4y+10xy^4\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"285\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Contoh polinomial homogen derajat 7:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b24c1a5bf1ed25c5698108cc448bdb4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y,z)=x^3y^4+2x^5y^2+4x^2y^2z^3-x^2y^4z\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"343\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Contoh polinomial homogen derajat 13: <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-50fee4914e8d236a46dbc69f8d67b3d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(a,b,c)=7a^6b^4c^3+2a^8b^3c^2+5a^4b^8c\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"297\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Polinomio-homogeneo-y-polinomio-heterogeneo\"><\/span> Polinomial homogen dan polinomial heterogen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Perlu dicatat bahwa polinomial lain yang sangat mirip dengan polinomial homogen adalah polinomial heterogen, meskipun terdapat perbedaan mendasar di antara keduanya:<\/p>\n<p> <strong>Polinomial heterogen<\/strong> adalah polinomial yang semua sukunya tidak mempunyai derajat yang sama.<\/p>\n<p> Oleh karena itu, hanya jika monomial dari polinomial tersebut mempunyai derajat yang berbeda dari unsur-unsur lainnya, polinomial tersebut akan menjadi heterogen.<\/p>\n<p> Misalnya, polinomial berikut ini heterogen:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8baa087cc08645b03a7879dc38522298_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y)=x^4+2x^3y+8x^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"202\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Meskipun dua suku dalam polinomial tersebut berderajat 4 (x <sup>4<\/sup> , 2x <sup>3<\/sup> y), sebenarnya polinomial tersebut merupakan polinomial heterogen karena mempunyai suku lain yang berderajat berbeda (8x <sup>2<\/sup> berderajat 2).<\/p>\n<p> Seperti yang Anda lihat, polinomial homogen dan heterogen sangat mirip satu sama lain dan mudah tertukar, jadi kita perlu berhati-hati. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Propiedades-de-los-polinomios-homogeneos\"><\/span> Sifat-sifat polinomial homogen<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Polinomial homogen mempunyai ciri-ciri sebagai berikut<\/p>\n<ul>\n<li> Banyaknya monomial homogen berderajat M yang berbeda dalam polinomial N variabel dapat dihitung dengan menggunakan rumus berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a50a9af76c5b398ccf1a017a08eb728c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{(M+N-1)!}{M!(N-1)!}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"107\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Mungkin \u201c <strong>!<\/strong> \u201d \u00bb terasa aneh bagi Anda karena digunakan dalam aljabar. Perlu Anda ketahui bahwa ini digunakan untuk menunjukkan operasi matematika khusus yang disebut <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/fungsi-faktorial-suatu-bilangan\/\">faktorial suatu bilangan<\/a><\/span><\/strong> . Anda dapat melihat terdiri dari apa operasi ini dan kegunaannya di tautan sebelumnya.<\/p>\n<ul>\n<li> Ekspresi deret Taylor yang berhubungan dengan polinomial homogen yang diperpanjang di titik <em>x<\/em> adalah sebagai berikut:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8f4fe67ef967d0006f8ec3f8936d3f1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x+y)= \\sum_{j=0}^n {n \\choose j}  \\check{P} (\\underbrace{x,x,\\dots ,x}_{j} &amp; \\underbrace{y,y,\\dots ,y}_{n-j})\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"346\" style=\"vertical-align: -30px;\"><\/p>\n<\/p>\n<p> Namun, untuk dapat menerapkan (dan memahami) properti ini, Anda perlu mengetahui cara penghitungan ekspresi<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4c062127739b922dff24815ba6bb3660_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} n \\\\ j \\end{pmatrix} ,\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"41\" style=\"vertical-align: -17px;\"><\/p>\n<p> disebut bilangan kombinatorial. Oleh karena itu, jika Anda belum memahami sifat-sifat sebelumnya, saya sarankan Anda melihat apa <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/sifat-koefisien-binomial-bilangan-kombinatorial\/\">rumus bilangan kombinatorial<\/a><\/span><\/strong> .<\/p>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Halaman ini menjelaskan apa itu polinomial homogen. Anda juga akan melihat contoh polinomial homogen dan sifat-sifat polinomial jenis ini. Selain itu, Anda juga akan menemukan perbedaan antara polinomial homogen dan polinomial heterogen. Apa yang dimaksud dengan polinomial homogen? Pengertian polinomial homogen adalah sebagai berikut: Dalam matematika, polinomial homogen adalah polinomial yang semua sukunya mempunyai derajat &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/\"> <span class=\"screen-reader-text\">Polinomial homogen<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[65],"tags":[],"class_list":["post-291","post","type-post","status-publish","format-standard","hentry","category-jenis-polinomial"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Polinomial homogen - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Polinomial homogen - Mathority\" \/>\n<meta property=\"og:description\" content=\"Halaman ini menjelaskan apa itu polinomial homogen. Anda juga akan melihat contoh polinomial homogen dan sifat-sifat polinomial jenis ini. Selain itu, Anda juga akan menemukan perbedaan antara polinomial homogen dan polinomial heterogen. Apa yang dimaksud dengan polinomial homogen? Pengertian polinomial homogen adalah sebagai berikut: Dalam matematika, polinomial homogen adalah polinomial yang semua sukunya mempunyai derajat &hellip; Polinomial homogen Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-06T18:20:29+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c562859bfcb9245bf750cdf62e30cc4_l3.png\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Polinomial homogen\",\"datePublished\":\"2023-07-06T18:20:29+00:00\",\"dateModified\":\"2023-07-06T18:20:29+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/\"},\"wordCount\":399,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Jenis polinomial\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/\",\"url\":\"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/\",\"name\":\"Polinomial homogen - 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Anda juga akan melihat contoh polinomial homogen dan sifat-sifat polinomial jenis ini. Selain itu, Anda juga akan menemukan perbedaan antara polinomial homogen dan polinomial heterogen. Apa yang dimaksud dengan polinomial homogen? Pengertian polinomial homogen adalah sebagai berikut: Dalam matematika, polinomial homogen adalah polinomial yang semua sukunya mempunyai derajat &hellip; Polinomial homogen Selengkapnya &raquo;","og_url":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/","article_published_time":"2023-07-06T18:20:29+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c562859bfcb9245bf750cdf62e30cc4_l3.png"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"2 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Polinomial homogen","datePublished":"2023-07-06T18:20:29+00:00","dateModified":"2023-07-06T18:20:29+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/"},"wordCount":399,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"articleSection":["Jenis polinomial"],"inLanguage":"id","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/","url":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/","name":"Polinomial homogen - Mathority","isPartOf":{"@id":"https:\/\/mathority.org\/id\/#website"},"datePublished":"2023-07-06T18:20:29+00:00","dateModified":"2023-07-06T18:20:29+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/#breadcrumb"},"inLanguage":"id","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/id\/contoh-polinomial-homogen\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/id\/"},{"@type":"ListItem","position":2,"name":"Polinomial homogen"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/id\/#website","url":"https:\/\/mathority.org\/id\/","name":"Mathority","description":"Di mana rasa ingin tahu bertemu dengan perhitungan!","publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/id\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"id"},{"@type":"Organization","@id":"https:\/\/mathority.org\/id\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/id\/","logo":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38","name":"Tim Mathority","image":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Tim Mathority"},"sameAs":["http:\/\/mathority.org\/id"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/291","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/comments?post=291"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/291\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/media?parent=291"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/categories?post=291"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/tags?post=291"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}