{"id":8950,"date":"2016-05-22T00:07:49","date_gmt":"2016-05-22T00:07:49","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8950"},"modified":"2016-05-22T00:07:49","modified_gmt":"2016-05-22T00:07:49","slug":"math-review-of-strategies-of-factoring-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2016\/05\/22\/math-review-of-strategies-of-factoring-polynomials\/","title":{"rendered":"Math Review of Strategies of Factoring Polynomials"},"content":{"rendered":"

Overview<\/h3>\n

As a general strategy for factoring polynomials, first check to see if there are any common factors.\u00a0 If there are not, check for the number of terms.\u00a0 If there are two terms, it may be a difference of squares.\u00a0 If there are three terms, it may be a perfect square of a binomial, or it may be possible to factor using a pattern.\u00a0 If there are four terms, it may be possible to factor by grouping.<\/p>\n

 <\/p>\n

Difference of Squares<\/h3>\n

An expression such as x2<\/sup> \u2013 36 follows a common pattern, as both x2<\/sup> and 36 are perfect squares.\u00a0 Recall that they can be factored as (x +6) (x -6), as the middle terms, 6x and -6x, cancel each other out.\u00a0 What about an expression such as 10x3<\/sup> \u2013 40x?\u00a0 First, factor out the common factor 10x(x2<\/sup> \u2013 4) because 10x \u00b7x2<\/sup> is 10x3<\/sup> and 10x\u00b74 is 40x.\u00a0 The expression x2<\/sup> -4 follows the pattern of a difference of squares, as (x+4) (x-4), so the entire factorization of 10x3<\/sup> \u2013 40x is 10x(x +4) (x-4).\u00a0 It is factored completely.<\/p>\n

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Perfect Square of a Binomial<\/h3>\n

An expression such as x6<\/sup> + 8x3<\/sup> +16, also follows a common pattern.\u00a0 The first term, x6<\/sup>, can be factored as a perfect square, x3<\/sup>\u00b7x3<\/sup>.\u00a0 Similarly, the last term, 16, can be factored as a perfect square, 4\u00b74.\u00a0 The middle term, 8x3<\/sup>, is 4x3<\/sup> + 4x3<\/sup>, so the expression x6<\/sup> + 8x3<\/sup> +16 can be factored as (x3<\/sup> +4) (x3<\/sup> +4).\u00a0 Recall the pattern of the perfect square of a binomial (a2<\/sup> +2ab + b2<\/sup>) equals (a + b) (a +b).<\/p>\n

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Factor Using a Pattern<\/h3>\n

Not all trinomials are perfect squares of a binomial.\u00a0 Some trinomials have a leading coefficient of 1, and they will factor as (x + __) (x + ___).\u00a0 Other trinomials have a leading coefficient of (__x + __) (___x + ___).\u00a0 Suppose the expression is 5x2<\/sup> + 15x +10.\u00a0 Each term has a common factor of 5(x2<\/sup> +3x + 2) which can be factored further as 5(x +1) (x +2).<\/p>\n

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Factor Four Terms by Grouping<\/h3>\n

Some expressions with four terms can be factored by grouping, just as trinomials can.\u00a0 For example, 6x3<\/sup> -9x2<\/sup> + 4x -6 can be factored by factoring each group.\u00a0 6x3<\/sup> -9x2 <\/sup>can be factored as 3x2<\/sup> (2x -3), and 4x -6 can be factored as 2(2x -3).\u00a0 The two groups can be combined as (2x -3) (3x2<\/sup> +2).<\/p>\n

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Overview As a general strategy for factoring polynomials, first check to see if there are any common factors.\u00a0 If there are not, check for the number of terms.\u00a0 If there are two terms, it may be a difference of squares.\u00a0 If there are three terms, it may be a perfect square of a binomial, or […]<\/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":[3935,3937,3936],"class_list":["post-8950","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-factoring-by-grouping","tag-factoring-by-patterns","tag-factoring-difference-of-squares"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8950","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=8950"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8950\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}