{"id":311,"date":"2012-02-12T21:13:13","date_gmt":"2012-02-13T02:13:13","guid":{"rendered":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/?p=311"},"modified":"2012-03-12T08:59:08","modified_gmt":"2012-03-12T12:59:08","slug":"math-7a-lesson-2-2122012","status":"publish","type":"post","link":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/2012\/02\/12\/math-7a-lesson-2-2122012\/","title":{"rendered":"Math 7A, Lesson 2, 2\/12\/2012"},"content":{"rendered":"<p>Today we continued to cover the content of factorization, with focus on factoring ax^2 + bx + c.<\/p>\n<p>If it can be factored, then we can write the following:<\/p>\n<p>ax^2 + bx +c = (mx + p) (nx + q) = mnx^2 + (mq+np)x + pq<\/p>\n<p>Then we have:<\/p>\n<p>a = mn<\/p>\n<p>b = mq + np<\/p>\n<p>c = pq<\/p>\n<p>That is, we want to find two factors m and n from a, so that a = mn, we want to find two factors p and q from c, so that c = pq, and such that the mq + np = b.<\/p>\n<p>If you list m, n, p, q the following way:<\/p>\n<p>m\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 p<\/p>\n<p>X<\/p>\n<p>n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 q<\/p>\n<p>It is the sum of the cross-product, m * q + n * p that must equal to b.<\/p>\n<p>We also talked abut factoring by group. For example:<\/p>\n<p>x^3 +2x^2 +3x +6 = x^2(x+2) + 3(x+2)\u00a0= (x+2)(x^2 + 2)<\/p>\n<p>Factorization takes time to get good at and only practice can get you there. So here is the homework:<\/p>\n<p><a href=\"http:\/\/blog.newtonchineseschool.org\/wangweidong\/files\/2012\/02\/Math7_Spring_HW_L2.pdf\">http:\/\/blog.newtonchineseschool.org\/wangweidong\/files\/2012\/02\/Math7_Spring_HW_L2.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Today we continued to cover the content of factorization, with focus on factoring ax^2 + bx + c. If it can be factored, then we can write the following: ax^2 + bx +c = (mx + p) (nx + q) = mnx^2 + (mq+np)x + pq Then we have: a = mn b = mq [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[4,10,3],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/311"}],"collection":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/comments?post=311"}],"version-history":[{"count":3,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/311\/revisions"}],"predecessor-version":[{"id":331,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/posts\/311\/revisions\/331"}],"wp:attachment":[{"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/media?parent=311"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/categories?post=311"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.newtonchineseschool.org\/wangweidong\/wp-json\/wp\/v2\/tags?post=311"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}