{"id":6856,"date":"2014-04-24T16:11:56","date_gmt":"2014-04-24T16:11:56","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=6856"},"modified":"2014-12-02T08:25:30","modified_gmt":"2014-12-02T08:25:30","slug":"math-review-of-finding-common-factors-of-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2014\/04\/24\/math-review-of-finding-common-factors-of-polynomials\/","title":{"rendered":"Math Review of Finding Common Factors of Polynomials"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

The process of finding common factors for polynomials is similar to the process of finding common factors for real numbers. Both can be written as prime factors.\u00a0 The greatest common factor may be numerical, the product of a real number and a variable, or a binomial expression.<\/p>\n

Finding Prime Factors of Real Numbers<\/strong><\/p>\n

There are two types of real numbers: prime numbers and composite numbers.\u00a0 Prime numbers such as 2, 3, 5, 7, 11, 13 and so on, are only divisible by themselves and 1.\u00a0 All other numbers are composite numbers, as the product of prime numbers.\u00a0 Factoring a real number is a process of determining its prime factors.\u00a0 Suppose the number is 756.\u00a0 Its factors can be approximated by dividing by 9 to equal 9 \u2219 84.\u00a0 Both 9 and 84 are composite numbers, so 9 can be factored as 32<\/sup>and 84 can be factored as 3\u22197\u221922<\/sup>.\u00a0 The prime factorization of 756 is then 22 \u2219 <\/sup>33<\/sup> \u2219 7.<\/p>\n

Finding Numerical Factors of Polynomials<\/strong><\/p>\n

Finding numerical factors of polynomials is a very similar process.\u00a0 Suppose the expression is 12x2<\/sup> + 4x + 8.\u00a0 It can be factored by finding the numerical factor that is common to all monomials in the expression.\u00a0 In this example, every term can be divided evenly by 4, or 4(3x2<\/sup> + x + 2).\u00a0 The real number 12 is factored as 22<\/sup>\u2219 3, the real number 4 is factored as 22<\/sup>, and the real number 8 is factored as 23<\/sup>, or 22<\/sup> \u2219 2.<\/p>\n

Finding Greatest Common Factors that Include Variables<\/strong><\/p>\n

Sometimes the greatest common factor includes both a numerical coefficient and a variable.\u00a0 Suppose the expression is 15y3<\/sup>+25y2<\/sup> + 10y.\u00a0 In that case, the polynomial can be factored as the product of a monomial and a polynomial, as 5y(3y2<\/sup> + 5y + 2).\u00a0 If the polynomial were 18x3<\/sup>y + 21x2<\/sup>y2<\/sup> + 33xy3<\/sup>, it could be factored as 3xy(9x2<\/sup> + 7xy + 11y2<\/sup>).<\/p>\n

Finding Greatest Common Factors that Include Binomials<\/strong><\/p>\n

Sometimes the greatest common factors have a binomial factor.\u00a0 Suppose the problem is by + bd + xy + dx.\u00a0 Each group can be factored further, as b(y + d) + x(y + d).\u00a0 Using the Distributive Property results in (b + x)(y + d).<\/p>\n

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Overview: The process of finding common factors for polynomials is similar to the process of finding common factors for real numbers. Both can be written as prime factors.\u00a0 The greatest common factor may be numerical, the product of a real number and a variable, or a binomial expression. Finding Prime Factors of Real Numbers There […]<\/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":[2622,2647,1926],"class_list":["post-6856","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-factoring-polynomials","tag-prime-factors","tag-variables"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6856","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=6856"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/6856\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=6856"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=6856"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=6856"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}