{"id":147512,"date":"2022-04-25T14:43:20","date_gmt":"2022-04-25T09:13:20","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?post_type=web-story&#038;p=147512"},"modified":"2022-08-19T22:19:19","modified_gmt":"2022-08-19T16:49:19","slug":"maths-polynomial-remainder-theorem-explained-with-examples","status":"publish","type":"web-story","link":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-polynomial-remainder-theorem-explained-with-examples\/","title":{"rendered":"Polynomial Remainder Theorem Explained With Examples"},"content":{"rendered":"<p><html amp=\"\" lang=\"en\"><head><meta charSet=\"utf-8\"\/><meta name=\"viewport\" content=\"width=device-width,minimum-scale=1,initial-scale=1\"\/><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0.js\"><\/script><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0\/amp-story-1.0.js\" custom-element=\"amp-story\"><\/script><link 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\"Segoe UI\", Roboto, Oxygen-Sans, Ubuntu, Cantarell, \"Helvetica Neue\", sans-serif;;\n                font-size: calc(4 * var(--story-page-vw));\n                line-height: 1.4;\n                word-break: break-word;\n                word-wrap: break-word;\n                overflow-wrap: break-word;\n              }\n              <\/style>\n<p><meta name=\"web-stories-replace-head-start\"\/><title>Polynomial Remainder Theorem Explained With Examples<\/title><link rel=\"canonical\" href=\"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-polynomial-remainder-theorem-explained-with-examples\/\"\/><meta name=\"web-stories-replace-head-end\"\/><\/head><body><amp-story standalone=\"\" publisher=\"Aakash BYJU&amp;#039;S Blog\" publisher-logo-src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/blue.png\" title=\"Polynomial Remainder Theorem Explained With Examples\" 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style=\"position:absolute;pointer-events:none;left:12.37864%;top:99.83819%;width:41.74757%;height:4.04531%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:1.1627906976744187% 1.1627906976744187% 1.1627906976744187% 1.1627906976744187% \/ 8% 8% 8% 8%;background-clip:content-box;background-color:rgba(0,0,0,0.7)\" id=\"el-04e06552-d26c-4932-9884-e5e7bf8857fb\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.12263808139534883% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.242718em;line-height:1.2;text-align:initial;padding:2.3255813953488373% 4.651162790697675%;color:#000000\"><span><span style=\"color: #fff\">BY Team Aakash Byju&#8217;s<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:12.13592%;top:94.82201%;width:75.48544%;height:4.36893%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6430868167202572% 0.6430868167202572% 0.6430868167202572% 0.6430868167202572% \/ 7.4074074074074066% 7.4074074074074066% 7.4074074074074066% 7.4074074074074066%\" id=\"el-1218f1ce-75f5-42e6-963c-18204e23e445\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.10399919614147875% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.372168em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span>Explained With Examples<\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-2.91262%;top:14.56311%;width:106.06796%;height:62.13592%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-e42c1831-0a9c-4632-a574-ef81b316fec2\">\n<div style=\"position:absolute;width:100%;height:202.31482%;left:0%;top:-25.84758%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-7-26.jpg\" alt=\"Mathematics-7 (26)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-7-26.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-7-26-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-7-26-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-7-26-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 48vh, 106vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:84.62783%;width:75.48544%;height:10.84142%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6430868167202572% 0.6430868167202572% 0.6430868167202572% 0.6430868167202572% \/ 2.9850746268656714% 2.9850746268656714% 2.9850746268656714% 2.9850746268656714%\" id=\"el-2b10a7c2-b6f6-480a-ba08-47f7351744cc\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.12660771704180088% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.453074em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span>Polynomial Remainder Theorem:<\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:8.25243%;top:84.62783%;width:2.91262%;height:19.41748%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-d029a117-c0f3-4d7e-b4e8-93943ac58b15\">\n<div class=\"fill\" style=\"background-color:#000;will-change:transform\"><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:11.65049%;height:7.76699%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-387fb96c-b6a9-4b80-b9b0-c80ce1eab74f\">\n<div style=\"position:absolute;width:100%;height:100.00004%;left:0%;top:-0.00002%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/blue.png\" alt=\"blue\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/blue.png 96w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/blue-75x75.png 75w\" sizes=\"(min-width: 1024px) 5vh, 12vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"ba32cf7f-c1a0-4cfc-8809-86014de66f4d\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-8aa2e2d9-1329-4b26-a5ff-eac343cab7ed\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a1dcfb7c-f778-4fcb-b3ec-b2b7e45b9b64\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":2000,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script 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template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:73.94822%;width:76.69903%;height:25.72816%;opacity:1\">\n<div id=\"anim-8aa2e2d9-1329-4b26-a5ff-eac343cab7ed\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.257861635220126% 1.257861635220126% 1.257861635220126% 1.257861635220126%\" id=\"el-dfc9af7b-d3c1-4d7d-b184-897688fe52db\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:1.3805379746835444% 0;font-family:&quot;BioRhyme&quot;,serif;font-size:0.404531em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #fff\">The polynomial remainder theorem is a polynomial division approach to the Euclidean theorem.&nbsp;<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-6.31068%;top:15.69579%;width:110.92233%;height:58.09061%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-23b88036-014b-4f38-890f-3e1cc26ff864\">\n<div style=\"position:absolute;width:100%;height:226.30766%;left:0%;top:-41.08398%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-1-30.jpg\" alt=\"Mathematics-1 (30)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-1-30.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-1-30-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-1-30-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-1-30-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 50vh, 111vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.16505%;top:4.53074%;width:76.69903%;height:6.31068%;opacity:1\">\n<div id=\"anim-a1dcfb7c-f778-4fcb-b3ec-b2b7e45b9b64\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-76d95b50-090f-4880-98a2-5d409230c3fe\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 5.128205128205128% 5.128205128205128% 5.128205128205128% 5.128205128205128%\" id=\"el-031b501d-ceea-4859-b944-533ae15b635f\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:1.3805379746835444% 0;font-family:&quot;BioRhyme&quot;,serif;font-size:0.404531em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span>&nbsp;Euclidean Theorem<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"25879f9c-7221-4db0-9faf-e0c6392f814e\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script 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style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.13308359621451105% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.485437em;line-height:1.2;text-align:center;padding:1.2618296529968454% 2.5236593059936907%;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">Click Here To Attend Free Trail Class<\/span><\/span><\/p>\n<p><\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG-1.png\" theme=\"light\"><a href=\"https:\/\/byjus-aakash.onelink.me\/GieR\/aakashwebstories\" rel=\"\">Download Aakash App<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"5f6d4ac7-d449-4eac-b768-878108025ca3\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-b6270776-2431-4735-aaf5-9edc8774687a\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:white;background-image:linear-gradient(0turn, #256b6f 0%, #d9b4bb 100%)\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-0373bfcf-1c00-47ab-b80e-72fdac3b02a1\">\n<div class=\"fill\" style=\"will-change:transform\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:69.57929%;width:76.69903%;height:28.15534%;transform:rotate(360deg);opacity:1\">\n<div id=\"anim-b6270776-2431-4735-aaf5-9edc8774687a\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.1494252873563218% 1.1494252873563218% 1.1494252873563218% 1.1494252873563218%\" id=\"el-aa44fcaf-8ca7-496d-80ed-c3e7f18853e5\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:1.2700949367088603% 0;font-family:&quot;BioRhyme&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">In this polynomial theorem, we divide a polynomial P(x) by a factor ( x \u2013 a), which may or may not be a polynomial element.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-7.28155%;top:5.50162%;width:112.13592%;height:59.06149%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-02f49ab5-969e-494b-8b2d-8dc56a35a4d3\">\n<div style=\"position:absolute;width:100%;height:225.02282%;left:0%;top:-19.09729%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-2-28.jpg\" alt=\"Mathematics-2 (28)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-2-28.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-2-28-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-2-28-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-2-28-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 50vh, 112vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"9e830f65-fa3f-4567-94ab-87d617324ae7\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-1b0a3922-0324-445b-b895-a7f1f19e7348\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:white;background-image:linear-gradient(0turn, #32805e 0%, #e8e3e4 100%)\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-0f0acb68-a294-4a7d-8d1a-04cf355669bb\">\n<div class=\"fill\" style=\"will-change:transform\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:76.69903%;width:76.69903%;height:14.72492%;transform:rotate(360deg);opacity:1\">\n<div id=\"anim-1b0a3922-0324-445b-b895-a7f1f19e7348\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 2.197802197802198% 2.197802197802198% 2.197802197802198% 2.197802197802198%\" id=\"el-37ea11a1-63b6-4978-a618-2ef034d0596b\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:1.2700949367088603% 0;font-family:&quot;BioRhyme&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">A smaller polynomial and a remainder can be found.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:0;top:0;width:99.75728%;height:67.1521%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-9218a420-5f65-4bd3-b56c-f567bf270053\">\n<div style=\"position:absolute;width:120%;height:211.27712%;left:-10%;top:-18.72784%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-6-24.jpg\" alt=\"\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-6-24.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-6-24-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-6-24-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-6-24-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"6a4d2440-2cbb-48aa-88cd-d73247d44836\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-2b031659-3ef4-48cb-8b72-3f8cc54e3664\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:white;background-image:linear-gradient(0turn, #18686f 0%, #6f183b 100%)\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-1f2bb800-aa67-4bf9-8b65-118a590be6e6\">\n<div class=\"fill\" style=\"will-change:transform\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:65.04854%;width:76.69903%;height:32.8479%;opacity:1\">\n<div id=\"anim-2b031659-3ef4-48cb-8b72-3f8cc54e3664\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 0.9852216748768473% 0.9852216748768473% 0.9852216748768473% 0.9852216748768473%\" id=\"el-84e78aa4-22eb-4d76-b1b1-9a85bbae3ae4\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:1.2700949367088603% 0;font-family:&quot;BioRhyme&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">\u2013 Then the remainder &nbsp;<\/span><br \/>\n<span style=\"color: #edf6f6\">&nbsp;&nbsp;that has been obtained<\/span><br \/>\n<span style=\"color: #edf6f6\">&nbsp;&nbsp;is a value of P(x) at&nbsp;<\/span><br \/>\n<span style=\"color: #edf6f6\">&nbsp;&nbsp;x = a, specifically P(a).<\/span><br \/>\n<span style=\"color: #edf6f6\">\u2013 So basically, x &#8211; a is the<\/span><br \/>\n<span style=\"color: #edf6f6\">&nbsp;&nbsp;divisor of P(x) if and<\/span><br \/>\n<span style=\"color: #edf6f6\">&nbsp;&nbsp;only if P(a) = 0.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:-6.06796%;top:0;width:110.92233%;height:59.38511%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-17349af0-b845-4f0c-8ee2-04ad62ee3a64\">\n<div style=\"position:absolute;width:100%;height:221.37452%;left:0%;top:-31.90224%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-4-25.jpg\" alt=\"Mathematics-4 (25)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-4-25.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-4-25-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-4-25-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-4-25-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 50vh, 111vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"bf1616ae-732f-4852-bd95-5ff1408d580d\" auto-advance-after=\"7s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-5fe4ddc9-c722-4b35-876a-4020f86e67a4\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.2, 0.6, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-86fcf4d0-66e4-45a1-9277-ea3b6f5bf63b\",\"keyframes\":{\"transform\":[\"translate3d(0px, 1211.52319%, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":600,\"easing\":\"cubic-bezier(0.2, 0.6, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#370421\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-229e51e8-eab4-48b6-8291-7cca212aede3\">\n<div style=\"position:absolute;width:107%;height:107%;left:-3.5%;top:-3.5%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-3-28.jpg\" alt=\"Mathematics-3 (28)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-3-28.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-3-28-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-3-28-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/04\/Mathematics-3-28-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 48vh, 107vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:3.39806%;width:76.69903%;height:8.73786%;opacity:1\">\n<div id=\"anim-5fe4ddc9-c722-4b35-876a-4020f86e67a4\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-86fcf4d0-66e4-45a1-9277-ea3b6f5bf63b\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(0px, 1211.52319%, 0)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 3.7037037037037033% 3.7037037037037033% 3.7037037037037033% 3.7037037037037033%\" id=\"el-f1ff951d-8327-443e-838c-d2fad54e2e55\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:1.9327531645569613% 0;font-family:&quot;BioRhyme&quot;,serif;font-size:0.566343em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">Example<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><\/amp-story><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The polynomial remainder theorem is a polynomial division approach to the Euclidean theorem.<\/p>\n","protected":false},"author":1,"featured_media":149674,"template":"","meta":{"web_stories_publisher_logo":224678,"web_stories_poster":[],"web_stories_products":[],"footnotes":""},"web_story_category":[2144,2352],"web_story_tag":[],"class_list":["post-147512","web-story","type-web-story","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Remainder Theorem of Polynomials Explained With 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