{"id":8838,"date":"2016-02-08T00:52:21","date_gmt":"2016-02-08T00:52:21","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8838"},"modified":"2016-02-08T00:52:21","modified_gmt":"2016-02-08T00:52:21","slug":"math-review-of-adding-and-subtracting-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2016\/02\/08\/math-review-of-adding-and-subtracting-polynomials\/","title":{"rendered":"Math Review of Adding and Subtracting Polynomials"},"content":{"rendered":"

Overview<\/h3>\n

Adding and subtracting polynomials is similar to adding and subtracting other expressions. \u00a0Terms can be combined using the Commutative and Associative properties for addition, then like terms can be added or subtracted as needed.<\/p>\n

Find Like Terms<\/h3>\n

Recall that like terms have the same variables and are at the same degree.\u00a0 If they have the same degree, the terms are raised to the same power.\u00a0 For example, 4x and 2x can be added or subtracted because they both have the variable x and no other. Addition of 4x + 2x equals one term, the monomial 6x.\u00a0 They are also at the same degree, because both 4x and 2x have the same exponent 1.\u00a0 The expressions 3x2<\/sup> and 4x both have the variable x, but they are not at the same degree, as 3x2<\/sup> has degree 2, and 4x has degree 1.\u00a0 Combining them will result in the polynomial expression 3x2<\/sup> +4x.<\/p>\n

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Use Properties<\/h3>\n

Polynomials can be rearranged using the Commutative Property without changing their value.\u00a0 For example, 4x + 2x has the same meaning as 2x +4x.\u00a0 This was already shown in rearranging polynomials in standard form, so that 5x + 6x3<\/sup> +109 +8x2<\/sup> can be rearranged to\u00a0 6x3<\/sup> +8x2<\/sup> + 5x + 109.\u00a0 The Associative Property also applies, so that (6x3<\/sup> +8x2<\/sup>) + (5x + 109) equals 6x3 <\/sup>+ (8x2<\/sup> + 5x + 109).\u00a0 The one thing to remember when using either property with polynomials is that the sign in front of each term must stay with that therm.\u00a0 Therefore, 8x2<\/sup> + 5x -109 + 6x3<\/sup> can be rearranged as 6x3<\/sup> +8x2<\/sup> +5x -109.<\/p>\n

Adding Polynomials<\/h3>\n

In order to add polynomials, first find like terms, rearrange them using the Commutative Property, and combine like terms using the Associative Property.\u00a0 For example, (2x2<\/sup>-x) +(x2<\/sup> +3x -1) have the like terms of 2x2 <\/sup>\u00a0+x2<\/sup>, -x +3x, and the constant -1.\u00a0 Notice that the negative signs stay with the terms \u2013x and -1.\u00a0 The new expression, using all the terms, is 2x2<\/sup> +x2<\/sup> \u2013x +3x -1.\u00a0 Combining terms, (2x2<\/sup> +x2<\/sup>) +(-x + 3x) -1 results in a new expression where (2x2 <\/sup>\u00a0+x2<\/sup>) can be replaced by 3x2<\/sup>, and \u00a0(-x +3x ) can be replaced by 2x , so the simplified expression is 3x2<\/sup> +2x -1.<\/p>\n

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Subtracting Polynomials<\/h3>\n

Subtracting is the inverse of addition, so the difference between adding and subtracting polynomials is that each term subtracted has the opposite sign.\u00a0 For example, -(2x3<\/sup> + 4x2<\/sup> +12x +42) is -2x3<\/sup>-4x2<\/sup>-12x -42 and \u2013(2x2<\/sup>-12x \u2013 36) is -2x2<\/sup> +12x +36.\u00a0 Therefore, (a4<\/sup>-2a) \u2013(3a4<\/sup> -3a -1) is the same thing as adding a4<\/sup> -2a -3a4<\/sup> +3a +1.\u00a0 Like terms can be arranged, so that a4<\/sup>-3a4<\/sup> -2a +3a +1is the same expression.\u00a0 Then like terms can be combined, as -2a4<\/sup> +a +1.<\/p>\n

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Overview Adding and subtracting polynomials is similar to adding and subtracting other expressions. \u00a0Terms can be combined using the Commutative and Associative properties for addition, then like terms can be added or subtracted as needed. Find Like Terms Recall that like terms have the same variables and are at the same degree.\u00a0 If they have […]<\/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":[3883,3732,3884],"class_list":["post-8838","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-adding-polynomials","tag-combining-like-terms","tag-subtracting-polynomials"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8838","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=8838"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8838\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8838"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8838"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8838"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}