{"id":5568,"date":"2013-03-07T17:58:40","date_gmt":"2013-03-07T17:58:40","guid":{"rendered":"http:\/\/SchoolTutoring.com\/help\/?p=5568"},"modified":"2014-12-02T08:27:04","modified_gmt":"2014-12-02T08:27:04","slug":"algebra-core-concepts-using-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/algebra-core-concepts-using-polynomials\/","title":{"rendered":"Algebra Core Concepts: Using Polynomials"},"content":{"rendered":"

Overview:\u00a0 What Are Polynomials?<\/strong>
\nPolynomials are a special type of mathematical expression created by adding and subtracting numbers and variables.\u00a0 They can be added, subtracted, multiplied, and many other operations.\u00a0 Expressions such as the number 2, 4a, b2<\/sup>, and 3x3<\/sup> are all monomials that can be combined into number sentences as polynomials.<\/p>\n

Variables, Constants, and Coefficients<\/strong>
\nAlgebra is based upon the interaction of constants and variables.\u00a0 Numbers such as 2, 4, and 5 always mean the same thing and can be combined in familiar operations.\u00a0 They are the basis of math facts.\u00a0 In polynomials, they are constants.\u00a0 Variables in math are letters that stand for other numbers, the a, b, c, and x, y, z of algebra.\u00a0 They can be replaced by many different values depending on the solution of the problem.\u00a0 Coefficients are special constants that combine with variables. In the monomial 3x3<\/sup>, 3 is the coefficient.<\/p>\n

Adding and Subtracting Polynomials<\/strong>
\nIn order to add or subtract polynomials, group like terms together.\u00a0 For example, when adding (4a +6b) + (2a-3b), first group the (4a +2a) and the (6b-3b) together.\u00a0 Then use the distributive property, to solve (4+2)a + (6-3)b, or 6a +3b.\u00a0 Subtraction is the inverse of addition.\u00a0 Positive integers become negative , and negative become positive.\u00a0 Suppose the sentences are (r+ 8s)-(r-5s).\u00a0 Grouping the rs together results \u00a0in r-r =0 \u00a0and 8s +5s = 13s.<\/p>\n

Multiplying Polynomials<\/strong>
\nWhen multiplying polynomials, use the distributive property, as well as exponents.\u00a0 For example, if a rectangle has one side 3x and another side (7x-9), to find the area, multiply the length by the width to find the area, or 3x(7x -9) = 3x(7x)+ 3x(-9) = 21x2<\/sup>-27x.<\/p>\n

Multiplying two polynomials involves using the distributive property twice.\u00a0 For example, multiply (x+2)(x-5) to equal (x+2)x + (x+2)(-5) or x2<\/sup>+ 2x -5x -10.\u00a0 A positive number multiplied by a negative number will result in a negative number. \u00a0Grouping like terms will result in x2<\/sup>+ (2x-5x) -10 or x2<\/sup>-3x-10.<\/p>\n

FOILed Again<\/strong>
\nIn order to help remember the order of multiplication of two polynomials, use the word FOIL to remember the first terms are combined first, then the outer terms, then the inner terms, then the last terms.\u00a0 For example, when multiplying (2x +5)(3x+4), first multiply 2x(3x) or 6x2<\/sup>, then 2x (4) or 8x, then 5(3x) or 15x, then 5(4) or 20.\u00a0 Adding like terms together, 6x2<\/sup> + (8x+ 15x), or 23x + 20.<\/p>\n

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Overview:\u00a0 What Are Polynomials? Polynomials are a special type of mathematical expression created by adding and subtracting numbers and variables.\u00a0 They can be added, subtracted, multiplied, and many other operations.\u00a0 Expressions such as the number 2, 4a, b2, and 3×3 are all monomials that can be combined into number sentences as polynomials. Variables, Constants, and […]<\/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":[304,391,671,1360,1926],"class_list":["post-5568","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-coefficients","tag-constants","tag-foil","tag-polynomials","tag-variables"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5568","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=5568"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5568\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=5568"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=5568"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=5568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}