{"id":6600,"date":"2014-02-18T17:06:37","date_gmt":"2014-02-18T17:06:37","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6600"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"math-review-of-monomials-and-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/02\/18\/math-review-of-monomials-and-polynomials\/","title":{"rendered":"Math Review of Monomials and Polynomials"},"content":{"rendered":"<p><strong>Overview:<\/strong><\/p>\n<p>Monomial and polynomial expressions in algebra are ways to combine numbers and variables within an equation.\u00a0 Both types of expressions follow certain rules. They can be used in operations, similar to other numbers.<\/p>\n<p><strong>What Are Monomials?<\/strong><\/p>\n<p>Monomials are numbers or variables, or the product of numbers and variables.\u00a0 The exponents must be positive whole numbers.\u00a0 For example, an expression such as 9 is a monomial because it is a single number.\u00a0 A variable such as z<sup>4<\/sup> is a monomial, because the exponent is a positive whole number.\u00a0 Similarly, &#8211; 3q<sup>9<\/sup>y<sup>2<\/sup> is a monomial, because the negative number, -3, is not in the exponent.<\/p>\n<p><strong>What Are Not Monomials?<\/strong><\/p>\n<p>An expression such as 8y<sup>-4<\/sup> is not a monomial.\u00a0 Although it has a whole number exponent, the exponent is negative.\u00a0 Similarly, 3y<sup>1\/2<\/sup> is not a monomial because the exponent is not a whole number.\u00a0 Also, an expression such as 4z<sup>2<\/sup>y + 1, is not a monomial, because it contains two separate monomials, 4z<sup>2<\/sup>y and 1.\u00a0 They are added together, rather than being the product of numbers and variables.<\/p>\n<p><strong>What Are Polynomials?<\/strong><\/p>\n<p>Polynomials are a larger set of algebraic expressions that include monomials.\u00a0 They can have more than one term, such as monomials added together.\u00a0 The expression 4z<sup>2<\/sup>y + 1 is the sum of monomials.\u00a0 It is called a binomial because it has two terms.\u00a0 Similarly, an expression such as 2a &#8211; 3n + 4 is a trinomial, because it has three terms that are added together as part of the same unit.<\/p>\n<p><strong>What Is the Degree of a Polynomial?<\/strong><\/p>\n<p>The degree of a polynomial is taken from the highest exponent used in its terms.\u00a0 For example, the expression 2x<sup>2<\/sup> + y + 4 has the highest exponent of 2 in the term 2x<sup>2<\/sup>.\u00a0 It is also known as a quadratic polynomial.\u00a0 Linear polynomials, such as 2z + 3 are also common.\u00a0 An expression such as 5x<sup>3<\/sup> + 1 is also known as a cubic polynomial.<\/p>\n<p>Interested in <a href=\"https:\/\/schooltutoring.com\/math-tutoring\/algebra-1-tutoring\/\">algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n<p><span class=\"tutorOrange\">SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in The Dalles, OR visit: <a href=\"https:\/\/schooltutoring.com\/tutoring-in-the-dalles-oregon\/\">Tutoring in The Dalles, OR<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Overview: Monomial and polynomial expressions in algebra are ways to combine numbers and variables within an equation.\u00a0 Both types of expressions follow certain rules. They can be used in operations, similar to other numbers. What Are Monomials? Monomials are numbers or variables, or the product of numbers and variables.\u00a0 The exponents must be positive whole [&hellip;]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[467,1145,1359],"class_list":["post-6600","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-degree-of-a-polynomial","tag-monomial","tag-polynomial"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6600","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=6600"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6600\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}