{"id":664464,"date":"2023-07-12T11:48:24","date_gmt":"2023-07-12T06:18:24","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=664464"},"modified":"2025-05-15T15:18:07","modified_gmt":"2025-05-15T09:48:07","slug":"types-of-polynomials","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/","title":{"rendered":"Types of Polynomials"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" 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href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Introduction_to_Polynomials\" title=\"Introduction to Polynomials\">Introduction to Polynomials<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Types_of_Polynomials\" title=\"Types of Polynomials\">Types of Polynomials<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Types_of_Polynomials_on_the_Basis_of_Degree\" title=\"Types of Polynomials on the Basis of Degree\">Types of Polynomials on the Basis of Degree<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Types_of_Polynomials_on_the_Basis_of_Terms\" title=\"Types of Polynomials on the Basis of Terms\">Types of Polynomials on the Basis of Terms<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Monomials\" title=\"Monomials\">Monomials<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Binomials\" title=\"Binomials\">Binomials<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Trinomials\" title=\"Trinomials\">Trinomials<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Special_Types_of_Polynomials\" title=\"Special Types of Polynomials\">Special Types of Polynomials<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Monic_polynomial\" title=\"Monic polynomial\">Monic polynomial<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Irreducible_polynomial\" title=\"Irreducible polynomial\">Irreducible polynomial<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Homogeneous_polynomial\" title=\"Homogeneous polynomial\">Homogeneous polynomial<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#FAQs_on_Types_of_Polynomials\" title=\"FAQs on Types of Polynomials\">FAQs on Types of Polynomials<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#What_is_a_Polynomial\" title=\"What is a Polynomial?\">What is a Polynomial?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#What_are_a_polynomials_terms_degrees_and_exponents\" title=\"What are a polynomial&#039;s terms, degrees, and exponents?\">What are a polynomial&#039;s terms, degrees, and exponents?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#What_is_the_standard_form_of_the_polynomial\" title=\"What is the standard form of the polynomial?\">What is the standard form of the polynomial?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/infinitylearn.com\/surge\/topics\/types-of-polynomials\/#Is_6_a_polynomial\" title=\"Is 6 a polynomial?\">Is 6 a polynomial?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><strong>Polynomials<\/strong> are usually classified on the basis of their degree and the number of terms in the expression. The degree of a polynomial is the highest power of the variable in the equation given. It determines the behavior and the shape of the graph plotted for the polynomial given.<br \/>\nAn example of a polynomial is :<\/p>\n<p><strong>f(x) = x\u00b2+2x-3<\/strong><\/p>\n<p>This polynomial has 3 terms in it.<br \/>\nHere, the <strong>degree of the polynomial<\/strong> is 2 since the term with the highest power of &#8216;x&#8217; is &#8216;x\u00b2&#8217;, therefore, 2 is the highest power hence the degree of the polynomial as well.<\/p>\n<p>This article will discuss different <strong>Types of Polynomials<\/strong>. Read the complete article for a better understanding of the types of polynomials.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Introduction_to_Polynomials\"><\/span>Introduction to Polynomials<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Polynomials<\/strong> are defined as the type of algebraic expressions whose variables have only non-negative integers as their powers.<\/p>\n<p>For example:<\/p>\n<p><strong>f(x) 5x\u00b2 &#8211; x + 1 is a polynomial.<\/strong><\/p>\n<p>The algebraic expression 3x\u00b3 + 4x + 5\/x + 6x\u00b3\/\u00b2 is not a polynomial, since one of the powers of &#8216;x&#8217; is a fraction and the other is negative.<\/p>\n<p>To know more about polynomials, check: Polynomials<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Types_of_Polynomials\"><\/span>Types of Polynomials<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>As previously mentioned, the polynomials can be classified in two ways:<\/p>\n<ol>\n<li>On the basis of the degree<\/li>\n<li>On the basis of the number of terms.<\/li>\n<\/ol>\n<p>The types of polynomials on the basis of degree are zero polynomial, linear, quadratic, and cubic polynomials.<br \/>\nThe types of polynomials on the basis of the number of terms: monomials, binomials, trinomials, etc.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Types_of_Polynomials_on_the_Basis_of_Degree\"><\/span>Types of Polynomials on the Basis of Degree<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The power of the leading term is called the degree of the polynomial. It is also defined as the highest power of the variable. The degree of the Polynomials is obtained by arranging all the terms of polynomials in the descending order of their powers.<br \/>\nOn the basis of the degree of the polynomial, the polynomials can be classified into 4 major types. The names are mentioned below.<\/p>\n<ul>\n<li>Zero or constant polynomial<\/li>\n<li>Linear polynomial<\/li>\n<li>Quadratic polynomial<\/li>\n<li>Cubic polynomial<\/li>\n<\/ul>\n<p>The below-mentioned table provides a clear explanation of the above-mentioned types of Polynomials.<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td style=\"text-align: center;\"><strong>Type of Polynomials <\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Definition<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Example<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Zero or Constant Polynomial<\/td>\n<td>Polynomials with 0 degrees.<\/td>\n<td>3x\u2070, 8y\u2070, 4z\u2070<\/td>\n<\/tr>\n<tr>\n<td>Linear Polynomial<\/td>\n<td>Polynomials with 1 as the highest degree.<\/td>\n<td>5x, 9y, 10x &#8211; 3y<\/td>\n<\/tr>\n<tr>\n<td>Quadratic Polynomial<\/td>\n<td>Polynomials with 2 as the highest degree.<\/td>\n<td>3x\u00b2, 7x\u00b2-4y+7<\/td>\n<\/tr>\n<tr>\n<td>Cubic Polynomial<\/td>\n<td>Polynomials with 3 as the highest degree.<\/td>\n<td>8x\u00b3, 9x\u00b3-6x\u00b2+4x-2<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Polynomials_on_the_Basis_of_Terms\"><\/span>Types of Polynomials on the Basis of Terms<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There is a division of polynomials with respect to the number of terms present in their respective expression. There are polynomials with one term, two terms, three terms, and even more. Based on the number of terms, the polynomials are classified as:<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Monomials\"><\/span>Monomials<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A monomial is a polynomial expression consisting of only a single term.<br \/>\nFor example: 4t, 21x, 2y, 9pq.<br \/>\nFurthermore, 2x + 8x + 1x is a monomial because these are like terms added together, resulting in 11x, a single term.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Binomials\"><\/span>Binomials<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A binomial is a polynomial expression with two, unlike terms.<br \/>\nFor example: 7x + x\u00b2 is a binomial as it contains two unlike terms, that is, 7x and x\u00b2.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Trinomials\"><\/span>Trinomials<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A trinomial is a polynomial expression with three, unlike terms.<br \/>\nFor example: 6x + 9x\u00b2 \u2013 12x\u00b3<\/p>\n<p>Polynomial expressions with more than 3 terms also exist. Polynomials that have 4, unlike terms, are called four-term polynomials.<br \/>\nSimilarly, polynomial expressions with 5 terms are called five-term polynomials, and so on.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Special_Types_of_Polynomials\"><\/span>Special Types of Polynomials<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Apart from the above-mentioned types of polynomials, some special types exist simultaneously.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Monic_polynomial\"><\/span>Monic polynomial<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A polynomial expression whose leading coefficient is 1.<br \/>\nExample: x\u00b3 + 3x + 3.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Irreducible_polynomial\"><\/span>Irreducible polynomial<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A polynomial that cannot be further factored into a lower-degree polynomial.<br \/>\nExample: x\u00b2 + 2 is an irreducible polynomial.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Homogeneous_polynomial\"><\/span>Homogeneous polynomial<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A polynomial expression whose all the terms have the same degree.<br \/>\nExample: x\u00b2 + xy + y\u00b2.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_Types_of_Polynomials\"><\/span>FAQs on Types of Polynomials<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_a_Polynomial\"><\/span>What is a Polynomial?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA polynomial is an expression consisting of variables (or indeterminate), exponents, and constants. For example, 3x2 -2x-10 is a polynomial. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_are_a_polynomials_terms_degrees_and_exponents\"><\/span>What are a polynomial&#039;s terms, degrees, and exponents?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIf 2x2 \u2013 3x +19 is a polynomial, then; Terms: 2x2,-3x & 19 Degree: 2 (the highest exponent of variable x) Exponents: Power raised to variable x, i.e. 2 and 1. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_standard_form_of_the_polynomial\"><\/span>What is the standard form of the polynomial?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA standard polynomial is one where the highest degree is the first term; subsequently, the other terms come. For example, x3 \u2013 3x2 + x -12 is a standard polynomial. So the highest degree in the given polynomial expression is 3, then comes 2, and then 1. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Is_6_a_polynomial\"><\/span>Is 6 a polynomial?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\t6 can be written as 6x0 or 0x2+0x+6, representing the polynomial expression. Therefore, we can consider 6 as a polynomial. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is a Polynomial?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A polynomial is an expression consisting of variables (or indeterminate), exponents, and constants. For example, 3x2 -2x-10 is a polynomial.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are a polynomial's terms, degrees, and exponents?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"If 2x2 \u2013 3x +19 is a polynomial, then; Terms: 2x2,-3x &amp; 19 Degree: 2 (the highest exponent of variable x) Exponents: Power raised to variable x, i.e. 2 and 1.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the standard form of the polynomial?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A standard polynomial is one where the highest degree is the first term; subsequently, the other terms come. For example, x3 \u2013 3x2 + x -12 is a standard polynomial. So the highest degree in the given polynomial expression is 3, then comes 2, and then 1.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Is 6 a polynomial?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"6 can be written as 6x0 or 0x2+0x+6, representing the polynomial expression. Therefore, we can consider 6 as a polynomial.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Polynomials are usually classified on the basis of their degree and the number of terms in the expression. The degree [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Types of Polynomials","_yoast_wpseo_title":"Types of Polynomials: Monomials, Binomials, and Trinomials","_yoast_wpseo_metadesc":"Polynomials is algebraic expressions whose variables have only non-negative integers as their powers. Types of Polynomials","custom_permalink":"topics\/types-of-polynomials\/"},"categories":[8594,8591],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Types of Polynomials: Monomials, Binomials, and Trinomials<\/title>\n<meta name=\"description\" content=\"Polynomials is algebraic expressions whose variables have only non-negative integers as their powers. 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