{"id":8920,"date":"2016-04-23T23:30:14","date_gmt":"2016-04-23T23:30:14","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=8920"},"modified":"2016-05-02T00:19:30","modified_gmt":"2016-05-02T00:19:30","slug":"math-review-of-factoring-special-polynomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/math-review-of-factoring-special-polynomials\/","title":{"rendered":"Math Review of Factoring Special Polynomials"},"content":{"rendered":"

Overview<\/h3>\n

Factoring polynomials in general is the reverse process of multiplying them, and then finding common factors.\u00a0 However, some polynomials follow special patterns, such as the difference of two squares and trinomial squares, leading to shortcut methods of factoring.<\/p>\n

Recognizing the Difference of Two Squares<\/h3>\n

In order for a polynomial to be the difference of two squares, there must be two terms in the polynomial (a binomial), both terms in the binomial must be perfect squares, and there must be a minus sign between them.\u00a0 For example, the binomial x2<\/sup> -16 has two terms in the binomial, there is a minus sign between them, and both x2<\/sup> and 16 are perfect squares, as the square root of x2<\/sup> is x, and the square root of 16 is 4.\u00a0 Suppose the polynomial were x4<\/sup> +81.\u00a0 Although it is a binomial, and both x4<\/sup> and 81 are perfect squares, there is a plus sign between them, so it doesn\u2019t satisfy all the conditions.\u00a0 Suppose the polynomial was 4x2<\/sup> \u2013 10.\u00a0 The monomial 4x2<\/sup> is a perfect square (2x), the expression is a binomial, and there is a minus sign between them.\u00a0 However, 10 is not a perfect square, so it is not the difference of two squares.\u00a0 Suppose the expression is -9x2<\/sup> +25.\u00a0 It can be turned around, using the commutative property, so that the expression becomes 25-9x2<\/sup>.\u00a0 It is a binomial, the minus sign is between the two terms, and both 25 and 9x2<\/sup> are perfect squares, as the square root of 25 is 5 and the square root of 9x2<\/sup> is 3x.<\/p>\n

\"\"<\/a><\/p>\n

Factoring the Difference of Two Squares<\/h3>\n

Recall from the discussion of special products of polynomials that the product of (x +y) (x-y) equals x2<\/sup> \u2013 y2<\/sup> because xy and \u2013xy cancel each other out.\u00a0 Therefore, a binomial such as x2<\/sup> \u2013y2<\/sup> can be factored so that it follows the pattern (x +y) (x-y).\u00a0 For example, the binomial 16x2<\/sup> \u2013 81 follows the pattern of the difference of two squares, and can be factored as (4x +9)(4x-9) because the square root of 16x2<\/sup> is 4x and the square root of 81 is 9.<\/p>\n

Recognizing Trinomial Squares<\/h3>\n

Trinomial squares also follow special conditions.\u00a0 Recall from the discussion of special products of polynomials that (x +y) 2<\/sup> is always a trinomial in the form of x2<\/sup> +2xy +y2<\/sup>.\u00a0 Similarly, (x-y) 2<\/sup> is always a trinomial in the form x2<\/sup> -2xy + y2<\/sup>.\u00a0 Therefore, a trinomial is a trinomial square if two of the terms are perfect squares, there are no minus signs before either of them, and the other term is twice the product of the first two.\u00a0 For example, x2<\/sup> +6x +9 fits the pattern because both x2 <\/sup>and 9 are perfect squares.\u00a0 The square root of x2<\/sup> is x, the square root of 9 is 3, and 3x + 3x is 6x.<\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

Factoring Trinomial Squares<\/h3>\n

After recognizing a trinomial square, it is a short step to factoring it.\u00a0 For example, since both x2<\/sup> and 9 are perfect squares, the square root of x2<\/sup> is x and the square root of 9 is 3.\u00a0 To check, multiply (x + 3) (x + 3) using FOIL, for x2<\/sup> + 3x +3x = 9, or x2<\/sup> + 6x +9.<\/p>\n

\"\"<\/a><\/p>\n

Interested in math tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Wichita, KS: visit:\u00a0 Tutoring in Wichita, KS<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview Factoring polynomials in general is the reverse process of multiplying them, and then finding common factors.\u00a0 However, some polynomials follow special patterns, such as the difference of two squares and trinomial squares, leading to shortcut methods of factoring. Recognizing the Difference of Two Squares In order for a polynomial to be the difference of […]<\/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":[496,2622,3921],"class_list":["post-8920","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-difference-of-two-squares","tag-factoring-polynomials","tag-factoring-trinomial-squares"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8920","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=8920"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/8920\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=8920"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=8920"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=8920"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}