tag:blogger.com,1999:blog-10220498.post8903226111738838782..comments2022-08-10T01:00:21.213-05:00Comments on Math Teacher Mambo: Factoring TrickShireen Dadmehrhttp://www.blogger.com/profile/16282965851939089408noreply@blogger.comBlogger22125tag:blogger.com,1999:blog-10220498.post-14851197620046176742017-09-07T08:06:17.972-05:002017-09-07T08:06:17.972-05:00But 4xx + 14x -8 and xx+ 14x -32 have nothing in c...But 4xx + 14x -8 and xx+ 14x -32 have nothing in common with each other...they have different y-intercepts, minimums and zeros. How are these mathematically connected, ie. why does this lead to the correct zeros and factors at the end?Jaimehttps://www.blogger.com/profile/01469025492506463406noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-24915491468622604732017-09-07T08:03:32.532-05:002017-09-07T08:03:32.532-05:00Why does this work? I'm good with the multipl...Why does this work? I'm good with the multiply to ac and add to b, as I usually teach factoring by grouping. What I do not understand is dividing those numbers by a, reducing - why does that give you the opposite of the zeros? I am not a fan of tricks so want to understand why this works. Thanks!Jaimehttps://www.blogger.com/profile/01469025492506463406noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-91624166897954887862016-12-21T15:25:30.194-06:002016-12-21T15:25:30.194-06:00What about -6v^2 - 11v -4 ? Help! What about -6v^2 - 11v -4 ? Help! Tpaquettehttps://www.blogger.com/profile/10438065191182010008noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-45984006286409778622015-08-14T17:27:06.801-05:002015-08-14T17:27:06.801-05:00Hi Sierra. That's from 2 x 14, the a term and ...Hi Sierra. That's from 2 x 14, the a term and the c term.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10220498.post-39507231258578621102015-08-14T14:13:30.009-05:002015-08-14T14:13:30.009-05:00Where did you get the 28 from?Where did you get the 28 from?Anonymoushttps://www.blogger.com/profile/17799722501397769769noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-39546553710999891042014-08-16T01:42:33.619-05:002014-08-16T01:42:33.619-05:00I like this.Please visit the website physicsisfunn...I like this.Please visit the website physicsisfunnyy.blogspot.com to improve your PCMDevendra Kumar Dubeyhttps://www.blogger.com/profile/13187005103413395144noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-40157217296756101832014-07-07T12:33:11.987-05:002014-07-07T12:33:11.987-05:00Don't forget GCF and it will work just fine.Don't forget GCF and it will work just fine. Tuxfordhttps://www.blogger.com/profile/02174289621794684514noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-34579102089389680582014-01-06T00:54:05.360-06:002014-01-06T00:54:05.360-06:004xx + 14x -8 can be worked using bottoms up witho...4xx + 14x -8 can be worked using bottoms up without grouping at the end.<br />Like the others rewrite as<br /> xx+ 14x -32 then factor<br />(x + 16)(x - 2) Divide the 16 and -2<br />by the lead coefficient 4 and get<br />(x + 16/4)(x - 2/4) Bottoms up<br />(x + 4)(2x - 1)<br />Multiply either binomial by the common factor 4 and get <br />(2x + 8)(2x-1) or (x+4)(4x -2)Anonymoushttps://www.blogger.com/profile/09893410742241290899noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-76794930628219015112013-11-21T17:11:15.405-06:002013-11-21T17:11:15.405-06:00what about 4m^2-4m-8
what about 4m^2-4m-8<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10220498.post-87609773112805472132013-07-10T09:37:05.564-05:002013-07-10T09:37:05.564-05:00This is awesome. Finally I have a new method that ...This is awesome. Finally I have a new method that I can share to my students. Thanks so much for sharing.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10220498.post-51040868368068607092013-03-12T12:57:51.813-05:002013-03-12T12:57:51.813-05:00This is great! My daughter is having the hardest t...This is great! My daughter is having the hardest time grasping <a href="http://www.jdfactors.com" rel="nofollow">factoring</a> and I've been looking for ways to help her out. I think she would love this!Anonymoushttps://www.blogger.com/profile/14411588007368223468noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-54947212370763526132012-11-08T10:23:50.230-06:002012-11-08T10:23:50.230-06:00Love it!! Awesome!!
I'll use it with my stude...Love it!! Awesome!!<br /><br />I'll use it with my students!!<br /><br />Thanks for sharing it!!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10220498.post-27274738725127521142012-08-16T10:10:47.708-05:002012-08-16T10:10:47.708-05:00cool! I have always trained with tic-tac-toe but t...cool! I have always trained with tic-tac-toe but this might be even simpler. Less guidelines to keep in mind for the kids!factoring companieshttp://www.invoicefactoringloans.com/factoring-companies/noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-59481944494745318082012-01-09T19:56:20.352-06:002012-01-09T19:56:20.352-06:00Less is more. Our tea length wedding dresses best ...Less is more. Our <b><a href="http://www.ambersbridal.com/wedding-dresses/tea-length-wedding-dresses.html" title="tea length wedding dresses" rel="nofollow">tea length wedding dresses</a></b> best interpret the concept of amber-like purity by highlighting nothing but the texture of sheer fabrics. Close-fitted <b><a href="http://www.ambersbridal.com/wedding-dresses/mermaid-wedding-dresses.html" title="mermaid wedding dresses" rel="nofollow">mermaid wedding dresses</a></b> in fine structured physique inspire the thought of Grecian beauty, together with the air of hope and confidence towards life ooze out. Just release yourself from the dazzling complexity and all lost in simplicity.vintage wedding dresshttp://www.ambersbridal.com/wedding-dresses/vintage-wedding-dresses.htmlnoreply@blogger.comtag:blogger.com,1999:blog-10220498.post-10628681608150934862011-04-20T23:23:17.214-05:002011-04-20T23:23:17.214-05:00Okay.. yes this does make sense. I'm not sure ...Okay.. yes this does make sense. I'm not sure now what we were doing wrong. But Great! Thank you so much! This is extremely helpful! :)Lisa Rowannoreply@blogger.comtag:blogger.com,1999:blog-10220498.post-87218605422247232262011-04-19T20:49:22.270-05:002011-04-19T20:49:22.270-05:00Well, the "6 x 4" goes on the "bott...Well, the "6 x 4" goes on the "bottom" and the "-11" goes on top. <br /><br />Then the factors of 24 that add to -11 are "-8 and -3". Then you have to divide both -8 and -3 by 6 and simplify to get: -4/3 and -1/2. This gives you (3x - 4)(2x - 1). Is that what you were getting? Maybe you forgot to divide by the x^2 coefficient (6)? Or .....<br /><br />This trick doesn't work if all the terms have a common factor to begin with (then you have to factor out and then multiply back in later).<br /><br />Let me know if this makes sense.Shireen Dadmehrhttps://www.blogger.com/profile/16282965851939089408noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-23309080441164231022011-04-19T17:33:34.869-05:002011-04-19T17:33:34.869-05:00I'm tutoring an 8th grader that was taught thi...I'm tutoring an 8th grader that was taught this method. It was working perfectly until we got to<br /><br />6x^2-11x+4<br /><br />I could figure out the problem in my head but could not figure out how to find the answer using this trick. I know there is a common factor... so does this method just not work at all for this problem??<br />And ideas?Lisa Rowannoreply@blogger.comtag:blogger.com,1999:blog-10220498.post-55486340149321123432010-04-11T14:58:20.125-05:002010-04-11T14:58:20.125-05:00I love the prediction nature of the lesson, that&#...I love the prediction nature of the lesson, that's wonderful, and I plan to copy it.<br /><br />However ...<br /><br />4x^2 + 14x - 8<br />So we need ab = -32 and a + b = 14<br /><br />That gives us 16 & -2<br /><br />so <br />4x^2 -2x + 16x - 8 = (2x+8)(2x-1)<br /><br />It works beautifully, despite the common factor, and there's absolutely no reason why it shouldn't.<br /><br />I'd never seen this method before until, after about 6 years of teaching I was shown it by an Italian student in my IB mathematics SL class. Looked like some crazy wacko magic thingummy, but it worked. I can't stand 'magic methods', FOIL drives me crazy because it's just another shortcut (like telling kids to line up the numbers on the right hand side for addition) for teaching something that doesn't develop understanding required later to multiply out things like (5x^2+3x+2)(2x^4-7x^3+5x^2 - 4x + 4) so I sat down and analysed it algebraically and boy is it clever. Now I teach it all the time.<br /><br />May I recommend that you go through the algebra for this with your students if you haven't done so already - it doesn't look like it from your blog post. Start from (ax + b)(cx + d) and work from there. In terms of developing an appreciation of the power of factorization, and in demystifying something 'magical' which in my opinion we must always do as far as mathematics is concerned (the magic in mathematics is in its power and its beauty, in understanding what lies behind the 'clever tricks') - this is a wonderful teaching moment.Davidhttps://www.blogger.com/profile/08074201742571759308noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-18685557386951138422010-04-05T12:48:27.488-05:002010-04-05T12:48:27.488-05:00the "bottoms up" method is different. I...the "bottoms up" method is different. I might show that next year. I use the factor by grouping as well. I use it for all factoring problems even when the coefficient of 'a' is one. It seems to cut back on the confusion.Mr. Whttps://www.blogger.com/profile/13282059797251178491noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-72279828944318014132010-04-03T23:30:20.008-05:002010-04-03T23:30:20.008-05:00I've taught this factoring using grouping late...I've taught this factoring using grouping lately, but just a few days ago Dave Cox posted about this on his blog (coxmath.blogspot.com). He calls it "bottom's up", because when you get that fraction after dividing through the "a", you bring the bottom up to the front of that factor. I love this! Definitely going to have to show my kids this.<br /><br />Thanks!KFousshttps://www.blogger.com/profile/04493982153040173831noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-82389707335107825642010-04-03T18:03:48.796-05:002010-04-03T18:03:48.796-05:00Oooh, what's the tic-tac-toe? ... Also, I forg...Oooh, what's the tic-tac-toe? ... Also, I forgot to mention, that this only works when the 3 terms share no common factor. So 2xx + 7x - 4 would work, but 4xx + 14x - 8 wouldn't.<br /><br />Ms. CookieShireen Dadmehrhttps://www.blogger.com/profile/16282965851939089408noreply@blogger.comtag:blogger.com,1999:blog-10220498.post-16784325646418521852010-04-03T16:30:17.249-05:002010-04-03T16:30:17.249-05:00cool! I have always taught with tic-tac-toe but th...cool! I have always taught with tic-tac-toe but this might be even easier. Less rules to remember for the kids!Jen @ lil Mop Tophttps://www.blogger.com/profile/01553255997211787278noreply@blogger.com