{"id":914,"date":"2012-02-24T16:09:52","date_gmt":"2012-02-24T16:09:52","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=914"},"modified":"2014-12-02T08:33:48","modified_gmt":"2014-12-02T08:33:48","slug":"factoring-quadratic-equation","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/02\/24\/factoring-quadratic-equation\/","title":{"rendered":"Factoring Quadratic Equation"},"content":{"rendered":"<p>A <strong>quadratic equation<\/strong> is a one-variable polynomial equation of the second degree whose general form is:<\/p>\n<p>ax<sup>2<\/sup> + bx + c = 0,<\/p>\n<p>where a, b and c are constants with a \u2260 0, and x represents a variable. A quadratic equation has two solutions, called roots. The two solutions may be or may not be distinct and may or may not be real. A quadratic equation can be solved by factoring. The method of factoring explained below is also called as decomposition method.<\/p>\n<p>Let\u2019s factor the equation 3x<sup>2<\/sup> + 8x + 4 using the steps given below.<\/p>\n<p>Here, a = 3, b = 8 and c = 4<\/p>\n<p>Step 1: Multiply the term a and the term c<\/p>\n<p>3 \u00d7 4 = 12<\/p>\n<p>Step 2: Find two numbers whose product is equal to the product of terms a and c (12) and add up to be term b (8)<\/p>\n<p>6 \u00d7 2 = 12 and 6 + 2 = 8<\/p>\n<p>Step 3: Rewrite the middle term with these two numbers<\/p>\n<p>3x<sup>2<\/sup> + 6x + 2x + 4<\/p>\n<p>Step 4: Factor the first two terms and last two terms separately<\/p>\n<p>3x<sup>2<\/sup> + 6x factor into 3x(x + 2)<\/p>\n<p>2x + 4 factor into 2(x + 2)<\/p>\n<p>Organize the equation so that you can take out the greatest common factor of the first two terms and the last two terms.<\/p>\n<p>3x<sup>2<\/sup> + 6x + 2x + 4 = 3x(x + 2) + 2(x + 2)<\/p>\n<p>Both factored groups should be the same. (x + 2)<\/p>\n<p>Step 5: Add the GCF\u2019s together and enclose them in parentheses next to the factored group.<\/p>\n<p>(3x + 2)(x + 2)<\/p>\n<p>So (3x + 2) and (x + 2) are the factors if the quadratic 3x<sup>2<\/sup> + 8x + 4.<\/p>\n<p>Factors can be solved by equating to 0 to find the roots of the equation.<\/p>\n<p>3x + 2 = 0;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x + 2 = 0<\/p>\n<p>3x = -2;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = -2<\/p>\n<p>x = -2\/3;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x = -2<\/p>\n<p>-2\/3 and -2 are the roots of the equation 3x<sup>2<\/sup> + 8x + 4<\/p>\n<p>SchoolTutoring Academy 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 Hamilton visit: <a href=\"\/private-tutoring-in-hamilton\/\">Tutoring in Hamilton<\/a>.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A quadratic equation is a one-variable polynomial equation of the second degree whose general form is: ax2 + bx + c = 0, where a, b and c are constants with a \u2260 0, and x represents a variable. A quadratic equation has two solutions, called roots. The two solutions may be or may not [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2,13],"tags":[461,647,651,1694],"class_list":["post-914","post","type-post","status-publish","format-standard","hentry","category-algebra","category-pre-algebra","tag-decompositionmethod","tag-factoringquadraticequation","tag-factorsofquadraticequation","tag-solvingquadraticequation"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/914","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\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=914"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/914\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=914"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}