{"id":8924,"date":"2016-04-24T05:03:51","date_gmt":"2016-04-24T05:03:51","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=8924"},"modified":"2016-04-24T05:03:51","modified_gmt":"2016-04-24T05:03:51","slug":"math-review-of-factoring-polynomials-2","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2016\/04\/24\/math-review-of-factoring-polynomials-2\/","title":{"rendered":"Math Review of Factoring Polynomials"},"content":{"rendered":"

Overview<\/h3>\n

Factoring polynomial expressions is similar to factoring special polynomials.\u00a0 The difference is that both elements do not have to be perfect squares.\u00a0 It is the reverse of multiplying two binomials by using FOIL.<\/p>\n

Factoring Trinomials<\/h3>\n

Trinomials of the form x2<\/sup> +bx +c, when c>0 have certain aspects in common.\u00a0 The coefficient of the squared term is 1, so the only form to factor is the variable itself, in this case x times x.\u00a0 The constant c is a positive value.\u00a0 If the constant c is a positive number, but not a perfect square, it may have a variety of factors.<\/p>\n

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Using FOIL in Reverse<\/h3>\n

In order to multiply two binomials, FOIL is used, for the first term, the outer terms, the inner terms, and the last terms.\u00a0 It is also useful when factoring trinomials, only it is used to unravel the trinomial.\u00a0 In these examples, the first term, x2<\/sup>, can be factored as x \u00b7x.\u00a0 The factorization will have the form of (x + ___) (x + ____), so that first term is already known in these examples.<\/p>\n

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The Constant Term<\/h3>\n

The constant term c has a fixed numeric value, so that the last terms in each binomial will be factors of c.\u00a0 Suppose the binomial is x2<\/sup> +7x +12.\u00a0 The constant 12 has a number of factors, as 12 \u00b71 is 12, 6\u00b72 is 12, and 3\u00b74 is also 12.\u00a0 The constant 12 also has negative factors, as -12\u00b7-1 is 12, \u00b7-6\u00b7-2 is 12, and -3\u00b7-4 is also 12.<\/p>\n

The Middle Terms<\/h3>\n

Since there are usually a number of factors for the constant, there has to be a way to narrow them down and choose the correct one.\u00a0 Recall that the inner terms and the outer terms are added, while the last terms are multiplied.\u00a0 In order for a pair of factors to work, they must be added so that their sum is the coefficient of the middle term of the trinomial.\u00a0 In this example, the coefficient of the middle term is 7.\u00a0 The first pair of factors, 12 +1, equals 13; the second pair, 6 +2, equals 8; and the third pair, 3 +4, equals 7.\u00a0 By substitution, x2<\/sup> +7x + 12 factors as (x +3) (x +4).<\/p>\n

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Overview Factoring polynomial expressions is similar to factoring special polynomials.\u00a0 The difference is that both elements do not have to be perfect squares.\u00a0 It is the reverse of multiplying two binomials by using FOIL. Factoring Trinomials Trinomials of the form x2 +bx +c, when c>0 have certain aspects in common.\u00a0 The coefficient of the squared […]<\/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":[2622,3903],"class_list":["post-8924","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-factoring-polynomials","tag-using-foil"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8924","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=8924"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/8924\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=8924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=8924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=8924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}