{"id":6766,"date":"2014-02-25T16:42:42","date_gmt":"2014-02-25T16:42:42","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6766"},"modified":"2014-12-02T08:25:32","modified_gmt":"2014-12-02T08:25:32","slug":"math-review-of-factoring-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-factoring-polynomials\/","title":{"rendered":"Math Review of Factoring Polynomials"},"content":{"rendered":"

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

Polynomials can be completely factored in a similar way to factoring other numbers and monomials.\u00a0 It is a process of finding the greatest common factors in the expression, paying close attention to the way the numbers and variables are distributed, and checking to see if the factored form is equivalent to the original expressions.\u00a0 There are also a number of common patterns that can be used as shortcuts to factoring.<\/p>\n

What Are the Greatest Common Factors?<\/strong><\/p>\n

Suppose the expression is 15y2<\/sup> + 12y.\u00a0 What factors do both 15y2<\/sup> and 12y have in common?\u00a0 The expression 15y2<\/sup> is equal to 3 \u2219 5 \u2219 y \u2219 y.\u00a0 The expression 12y is equal to 3 \u2219 4 \u2219 y.\u00a0 Both 15y2<\/sup> and 12y have a common factor of 3y, as 15y2 <\/sup>is equal to 3y(5y) and 12y is equal to 3y(4).<\/p>\n

How Are the Numbers and Variables Distributed?<\/strong><\/p>\n

An expression like 15y2<\/sup> + 12y can be factored as 3y(5y) + 3y(4).\u00a0 Using the distributive property, that expression is equivalent to 3y(5y + 4), Suppose you had a rectangle with one side measuring 3y and the other side measuring 5y + 4.\u00a0 The area of the rectangle would be 3y(5y + 4) or 15y2<\/sup> + 12y.<\/p>\n

What Is the Opposite of FOIL?<\/strong><\/p>\n

In order to expand a polynomial expression such as (y + 2)(y + 4), the FOIL method is used.\u00a0 The first members, y and y, are multiplied as y2<\/sup>. The outside members, y(4), are multiplied as 4y, and the inside members 2y.\u00a0 Since 2y can be added to 4y, the middle term is 6y.\u00a0 The last term is 2(4) or 8.\u00a0 The entire expansion is y2<\/sup> + 6y + 8.\u00a0 Factoring is like the nonsense word LOIF.\u00a0 The last term, will be the product of two numbers that equal 8.\u00a0 The outside and inside terms will add together to equal 6, and the first term in this case will be the common factor of y \u2219 y, which simply y.\u00a0 Another way to say this is that the coefficient of the first y is 1 and the coefficient of the second y is 1 and 1 \u2219 1 equals 1.\u00a0 What numbers can be added to equal 6 and multiplied to equal 8?\u00a0 The answer would be 2 and 4 because 2 + 4 equals 6 and 2(4) equals 8.\u00a0 Using the distributive property y2 <\/sup>+6y + 8 is equivalent to (y + 4)(y + 2)<\/p>\n

What Are Some Common Patterns?<\/strong><\/p>\n

Some of the most common patterns of trinomials have shortcuts to factoring.\u00a0 One of these patterns is the difference of 2 squares, such as 4x2<\/sup> \u2013 25.\u00a0 It can be factored quickly by thinking about FOIL and LOIF.\u00a0 According to FOIL, the expanded form is (first term)(first term) + (last term)(-last term).\u00a0 The outside term and the inside term cancel each other out. The last term would be the negative square root times the positive square root, in order that the sign will be negative.\u00a0 According to LOIF, the last term is (-5)(5), or -25, the outside and inside terms will be 5x – 5x (equaling 0) and the first term is 2x.\u00a0 Factoring the expanded trinomial gives (2x + 5)(2x – 5), or 4x2<\/sup>-10x + 10x – 25, in simplest terms 4x2<\/sup> – 25.<\/p>\n

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Overview: Polynomials can be completely factored in a similar way to factoring other numbers and monomials.\u00a0 It is a process of finding the greatest common factors in the expression, paying close attention to the way the numbers and variables are distributed, and checking to see if the factored form is equivalent to the original expressions.\u00a0 […]<\/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":[2622,671,751,2623],"class_list":["post-6766","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-factoring-polynomials","tag-foil","tag-greatest-common-factor","tag-loif"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6766","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=6766"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6766\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6766"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6766"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}