{"id":5678,"date":"2013-03-26T15:00:18","date_gmt":"2013-03-26T15:00:18","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=5678"},"modified":"2014-12-02T08:27:04","modified_gmt":"2014-12-02T08:27:04","slug":"how-to-factoring-square-trinomials","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/how-to-factoring-square-trinomials\/","title":{"rendered":"How to: Factoring Square Trinomials"},"content":{"rendered":"

Overview:\u00a0 What Are \u00a0Square Trinomials?<\/strong>
\nSquare trinomials are polynomials in the form ax2<\/sup> + bx +c.\u00a0 They have three terms, with the highest degree a squared exponent.\u00a0 They are factored by multiplying binomials.<\/p>\n

Perfect Square Trinomials<\/strong>
\nA perfect square trinomial is the exact square of a trinomial.\u00a0 There are two conditions they follow.\u00a0 The first and last terms must be squares of binomials.\u00a0 Also, the middle term must be twice the product of the monomials.\u00a0 For example, x2<\/sup> – 14x + 49 and x2<\/sup> + 14x + 49 are both perfect square trinomials.\u00a0 Both x2<\/sup> and 49 are perfect squares.\u00a0 In addition, (1 x7) x 2 =14.<\/p>\n

Factoring Perfect Square Trinomials<\/strong>
\nFactoring x 2 <\/sup>-14x\u00a0 + 49 follows those rules. \u00a0First, find the square root of the outside terms, so that the square root of x2<\/sup> is x, and the square root of 49 is 7.\u00a0 Because it is a perfect square, the sign between the terms is the same as the sign of the middle term.\u00a0 Therefore, it is (x-7)(x-7).\u00a0 If the trinomial were x2<\/sup> + 14x +49, it would factor as (x +7)(x +7).<\/p>\n

When Trinomials Are Not a Perfect Square<\/strong>
\nNot all polynomials are a perfect square, even when the first term is squared.\u00a0 These polynomials are very similar.\u00a0 For example, x2<\/sup> + 5x + 6 can be factored as (x +2)(x +3).\u00a0 Remember the FOIL method?\u00a0 It can be applied backward to factor, as the first term has the factors 1 and x, the outside is 3x, the inside is 2x and the last term, 6, has the factors 2 and 3.<\/p>\n

The Difference Between Two Squares Is Also a Square Trinomial<\/strong>
\nThe number sentence a2<\/sup>-b2<\/sup> can be factored as (a + b)( a- b), as a special type of square trinomial.\u00a0 The middle terms just cancel one another out.\u00a0 Suppose the sentence to expand is 4x2<\/sup> – 49.\u00a0 It can be factored as (2x -7)(2x +7).\u00a0 The first term is 2x(2x) or 4x2<\/sup>, the outer term is 7(2x) or 14x, the inner term is -7(2x) or -14x, and the last term is -49.<\/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 Papillion, NE visit: Tutoring in Papillion, NE<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Overview:\u00a0 What Are \u00a0Square Trinomials? Square trinomials are polynomials in the form ax2 + bx +c.\u00a0 They have three terms, with the highest degree a squared exponent.\u00a0 They are factored by multiplying binomials. Perfect Square Trinomials A perfect square trinomial is the exact square of a trinomial.\u00a0 There are two conditions they follow.\u00a0 The first […]<\/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":[645,672,1717],"class_list":["post-5678","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-factoring","tag-foil-method","tag-square-trinomials"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5678","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=5678"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/5678\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=5678"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=5678"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=5678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}