{"id":61,"date":"2023-09-17T07:21:59","date_gmt":"2023-09-17T07:21:59","guid":{"rendered":"https:\/\/mathority.org\/id\/nilai-numerik-dari-contoh-polinomial-latihan-yang-diselesaikan\/"},"modified":"2023-09-17T07:21:59","modified_gmt":"2023-09-17T07:21:59","slug":"nilai-numerik-dari-contoh-polinomial-latihan-yang-diselesaikan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/nilai-numerik-dari-contoh-polinomial-latihan-yang-diselesaikan\/","title":{"rendered":"Nilai numerik polinomial"},"content":{"rendered":"<p>Di halaman ini Anda akan mengetahui apa itu dan bagaimana cara menghitung nilai numerik suatu polinomial. Selain itu, Anda akan dapat melihat contoh dan latihan yang diselesaikan selangkah demi selangkah dari nilai numerik suatu polinomial. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-valor-numerico-de-un-polinomio\"><\/span> Berapa nilai numerik polinomial?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Dalam matematika, nilai numerik suatu polinomial P(x) untuk nilai x=a, yaitu P(a), adalah hasil yang diperoleh dengan mengganti variabel x dari polinomial tersebut dengan bilangan a dan melakukan perhitungan yang ditunjukkan dalam ekspresi polinomial.<\/strong><\/p>\n<p> Agar Anda dapat lebih memahami konsep nilai numerik suatu polinomial, di bawah ini kami tunjukkan cara menghitungnya dengan sebuah contoh: <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Como-calcular-el-valor-numerico-de-un-polinomo\"><\/span> Cara menghitung nilai numerik polinomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Sekarang setelah kita mengetahui definisi matematis dari nilai numerik suatu polinomial, mari kita lihat cara menentukan nilai numerik suatu polinomial menggunakan sebuah contoh:<\/p>\n<ul>\n<li> Berapakah nilai numerik polinomial berikut untuk x=2?<\/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-65a7367fb9064a872fa5606d70d8327f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^3+5x^2-4x+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"198\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk mencari nilai numerik suatu polinomial, polinomial tersebut perlu dievaluasi dengan nilai yang diberikan oleh soal, yaitu perlu mensubstitusikan variabel tersebut.<\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> polinomial dengan nilai pernyataan. Oleh karena itu, dalam hal ini kita perlu mengganti surat tersebut<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Untuk 2:<\/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-8850b99aa8c1921c96f582d9cf2d372b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=2^3+5\\cdot 2^2-4\\cdot 2+1\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"218\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan setelah kita mengganti nilainya ke dalam ekspresi aljabar polinomial, kita melakukan operasinya. Jadi pertama-tama kita selesaikan kekuatannya:<\/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-9f1eb984d1fa73d02b5bed9ded3be62e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=8+5\\cdot 4-4\\cdot 2+1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"203\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sekarang kita menghitung perkaliannya:<\/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-162adaa6ea3726b7b0dd530232af86b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2)=8+20-8+1\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan terakhir, kita menjumlahkan dan mengurangi suku-sukunya:<\/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-06e073969fc5e5b3027491d9ef7ac94b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P(2)=21}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kesimpulannya, nilai numerik polinomial untuk x=2 sama dengan 21.<\/p>\n<p> Seperti yang Anda lihat, mencari nilai numerik suatu polinomial tidak terlalu rumit, namun memiliki beberapa penerapan yang sangat berguna. Misalnya, mengetahui cara mencari nilai numerik suatu polinomial sangat penting agar dapat menggunakan teorema sisa, sebuah teorema yang sangat penting tentang polinomial. Klik tautan ini dan cari tahu <a href=\"https:\/\/mathority.org\/id\/contoh-teorema-sisa-dan-latihan-diselesaikan\/\"><strong><span style=\"text-decoration: underline;\">apa teorema sisanya<\/span><\/strong><\/a> , Anda akan menemukan penjelasannya, contoh penggunaan, dan latihan yang diselesaikan langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplos-de-valores-numericos-de-polinomios\"><\/span> Contoh Nilai Numerik Polinomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Agar Anda memahami cara mendapatkan nilai numerik polinomial, kami memberikan contoh penyelesaian lainnya:<\/p>\n<h3 class=\"wp-block-heading\"> Contoh 1<\/h3>\n<ul>\n<li> Hitung nilai numerik polinomial\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f620a315934a4ae3ceb6dfe0d8b65130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=x^3-2x^2+3x+6\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"199\" style=\"vertical-align: -5px;\"><\/p>\n<p> Untuk<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6de4e73609a66312d9714a253f9ae3a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=-1.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"61\" style=\"vertical-align: 0px;\"><\/p>\n<\/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-3293713c5e12fac56d94be90f6bfc6e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(-1) &amp; =(-1)^3-2\\cdot (-1)^2+3\\cdot (-1)+6 \\\\[2ex] &amp; = -1-2\\cdot 1+3\\cdot (-1)+6 \\\\[2ex] &amp; =-1-2-3+6 \\\\[2ex]&amp;= \\bm{0} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"316\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dalam hal ini, nilai numerik polinomial sama dengan 0. Hal ini mempunyai konsekuensi karena sifat-sifat polinomial, karena berkat <strong><span style=\"text-decoration: underline;\"><a href=\"https:\/\/mathority.org\/id\/teorema-faktor\/\">teorema faktor<\/a><\/span><\/strong> kita dapat mengetahui berapa sisa pembagian tertentu antar polinomial. Untuk mempelajari lebih lanjut, klik tautan sebelumnya, di mana kami menjelaskan apa teorema ini dan kegunaannya.<\/p>\n<h3 class=\"wp-block-heading\"> Contoh 2<\/h3>\n<ul>\n<li> Tentukan nilai numerik polinomial\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-603996e6452fa70f3c1507d146c439e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=-2x^3+7x^2-8x-2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"221\" style=\"vertical-align: -5px;\"><\/p>\n<p> Untuk<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bf60bc9fcf312a246a055c15ee98033c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=3.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/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-ad8b1145d569157b4e771adfae674e2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(3) &amp; =-2\\cdot 3^3+7\\cdot 3^2-8\\cdot 3-2 \\\\[2ex] &amp; =-2\\cdot 27+7\\cdot 9-8\\cdot 3-2 \\\\[2ex] &amp; =-54+63-24-2 \\\\[2ex]&amp;= \\bm{-17} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"254\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Sejauh ini kita hanya melihat cara menentukan nilai numerik suatu polinomial dengan cara klasik, namun perlu Anda ketahui bahwa ada cara lain. Lebih khusus lagi, Anda juga dapat menghitung nilai numerik suatu polinomial dengan <a href=\"https:\/\/mathority.org\/id\/aturan-diselesaikan-contoh-latihan-ruffini\/\"><strong><span style=\"text-decoration: underline;\">metode Ruffini<\/span><\/strong><\/a> . Anda juga harus mengetahui cara menggunakan prosedur ini, jadi kami sarankan untuk membaca penjelasan detailnya di tautan. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Valor-numerico-de-un-polinomio-con-dos-o-mas-variables\"><\/span> Nilai numerik polinomial dengan dua variabel atau lebih<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Kita baru saja melihat cara mencari nilai numerik suatu polinomial jika polinomial tersebut hanya mempunyai satu variabel. Tapi\u2026 bagaimana cara mendapatkan nilai numerik suatu polinomial jika polinomial tersebut memiliki lebih dari satu variabel?<\/p>\n<p> Nah, jika suatu polinomial memiliki 2 huruf atau lebih, maka nilai numeriknya harus dihitung dengan cara yang sama, <strong>yaitu ganti dulu setiap variabel dalam polinomial tersebut dengan nilai yang sesuai, lalu selesaikan operasi polinomialnya<\/strong> .<\/p>\n<p> Sebagai contoh, Anda mempunyai masalah seperti ini yang diselesaikan di bawah ini:<\/p>\n<ul>\n<li> Temukan nilai numerik polinomial multivariat\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4ae6ce41951c6622a5dd702a3f74de67_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y)=x^2y+4xy-2x^2+6y-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"274\" style=\"vertical-align: -5px;\"><\/p>\n<p> untuk nilai-nilai<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-56213aa9361c3f660a6fd780c629a637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=2, y=3.\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"96\" style=\"vertical-align: -4px;\"><\/p>\n<\/li>\n<\/ul>\n<p> Pertama, kita ganti setiap variabel dengan nilainya yang sesuai, yaitu kita mengganti hurufnya<\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> untuk 2 dan kami mengubah surat itu<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> oleh 3:<\/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-a0a147fbd9eac856732e746ba31bf7ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,3)=2^2\\cdot 3+4\\cdot 2\\cdot 3-2\\cdot 2^2+6\\cdot 3-5\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"331\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kami memecahkan kekuatan:<\/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-4e196dd787140ebfd9cf51cd22665242_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,3)=4\\cdot 3+4\\cdot 2\\cdot 3-2\\cdot 4+6\\cdot 3-5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"315\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sekarang kita menghitung produknya:<\/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-d086e387e69df272c991d246a5419289_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(2,3)=12+24-8+18-5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"234\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan terakhir, kita melakukan penjumlahan dan pengurangan:<\/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-a56aaa1a35d10261d6a7c885d4c5c38c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P(2,3)=41}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"94\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Jadi nilai numerik polinomial untuk data instruksi setara dengan 41. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejercicios-resueltos-del-valor-numerico-de-un-polinomio\"><\/span> Menyelesaikan latihan tentang nilai numerik polinomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Berapa nilai numerik polinomial P(x) untuk x=-2? <\/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-2058e4637803a44f702503177a9a5999_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=-2x^3-4x^2+3x+8\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"222\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mencari nilai numerik polinomial, kita hanya perlu mensubstitusikan nilai yang diberikan dalam pernyataan ke dalam ekspresi polinomial dan menyelesaikan operasi yang dihasilkan: <\/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-93b7cf1a6c7e930a0a70fc8302f4012d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(-2) &amp; =-2\\cdot (-2)^3-4\\cdot (-2)^2+3\\cdot (-2)+8 \\\\[2ex] &amp; =-2\\cdot (-8)-4\\cdot 4+3\\cdot (-2)+8 \\\\[2ex] &amp; =+16-16-6+8 \\\\[2ex]&amp;= \\bm{2} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"351\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 2<\/h3>\n<p> Hitung nilai numerik polinomial berikut dengan pecahan untuk x=4. <\/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-51b55d638c13c2ae521dd1b268e566b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)=\\cfrac{1}{2} x^2-\\cfrac{5}{4}x + 7\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"163\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Baik polinomial tersebut memiliki pecahan atau tidak, prosedur untuk mencari nilai numerik polinomial tersebut selalu sama. Oleh karena itu kita harus mengganti variabel x dengan 4 dan menyelesaikan perhitungannya: <\/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-04fa4389b5e7c5257937ad35aed07c7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(4) &amp; =\\cfrac{1}{2} \\cdot 4^2-\\cfrac{5}{4}\\cdot 4+ 7 \\\\[2ex] &amp; =\\cfrac{1}{2} \\cdot 16-\\cfrac{5}{4}\\cdot 4+ 7\\\\[2ex] &amp; =8-5+7 \\\\[2ex]&amp;= \\bm{10} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"181\" width=\"186\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 3<\/h3>\n<p> Tentukan nilai numerik polinomial untuk nilai x=3, y=5 dan z=-2 <\/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-93ec397c7da59b30a0550f40bb0b1c06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x,y,z)=x^2yz+4y^2z^2-3x^2z+6xyz\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"312\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk menentukan nilai numerik polinomial multivariat, cukup dengan mengganti nilai yang diberikan dalam soal ke dalam ekspresi aljabar dan menyelesaikan operasi yang dihasilkan: <\/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-29683a91c14427a8ea42c3518e59e53f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(3,5,-2) &amp; =3^2\\cdot 5\\cdot (-2)+4\\cdot 5^2\\cdot (-2)^2-3\\cdot 3^2\\cdot (-2)+6\\cdot 3\\cdot 5 \\cdot (-2) \\\\[2ex] &amp; =9\\cdot 5\\cdot (-2)+4\\cdot 25\\cdot 4-3\\cdot 9\\cdot (-2)+6\\cdot 3\\cdot 5 \\cdot (-2) \\\\[2ex] &amp; =-90+400+54-180\\\\[2ex]&amp;= \\bm{184} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"142\" width=\"543\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Mengingat polinomial<\/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-288097fb1db706c4470871749ac23d88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(x)= -2x^3-3x^2+5x+k\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"222\" style=\"vertical-align: -5px;\"><\/p>\n<p> menghitung nilai parameter<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> sehingga <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3029b4a44964ce05fcd5497240a906ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2)=5.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__DDF5FF\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#DDF5FF\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>Lihat solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dalam soal ini, untuk mencari nilai yang tidak diketahui<\/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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> kita perlu menyelesaikan persamaan tersebut<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3029b4a44964ce05fcd5497240a906ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2)=5.\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -5px;\"><\/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-1c57342c839d903ba49d3065a69b092c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kita coba hitung dulu nilai P(-2):<\/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-3b58398099c8033b93a559e2f0c87f1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} P(-2) &amp; =-2\\cdot (-2)^3-3\\cdot (-2)^2+5\\cdot (-2)+k \\\\[2ex] &amp; =-2\\cdot (-8)-3\\cdot 4+5\\cdot (-2)+k \\\\[2ex] &amp; =+16-12-10+k\\\\[2ex]&amp;=-6+k \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"144\" width=\"351\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita menyamakan ekspresi yang diperoleh dengan 5: <\/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-1c57342c839d903ba49d3065a69b092c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-2)=5\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\"><\/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-e8b31008f76f38998d02a91cb976653e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-6+k=5\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan akhirnya, kita selesaikan persamaan yang dihasilkan: <\/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-9b76441987dd8c22187ed4d37c72baea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=5+6\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -2px;\"><\/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-30a3a62912d260d4dff9a56341e1e046_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{k=11}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<div id=\"ezoic-pub-ad-placeholder-176\" data-inserter-version=\"-1\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan mengetahui apa itu dan bagaimana cara menghitung nilai numerik suatu polinomial. Selain itu, Anda akan dapat melihat contoh dan latihan yang diselesaikan selangkah demi selangkah dari nilai numerik suatu polinomial. Berapa nilai numerik polinomial? Dalam matematika, nilai numerik suatu polinomial P(x) untuk nilai x=a, yaitu P(a), adalah hasil yang diperoleh &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/nilai-numerik-dari-contoh-polinomial-latihan-yang-diselesaikan\/\"> <span class=\"screen-reader-text\">Nilai numerik polinomial<\/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":[48],"tags":[],"class_list":["post-61","post","type-post","status-publish","format-standard","hentry","category-polinomial"],"yoast_head":"<!-- This site is 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