tag:blogger.com,1999:blog-1091979517567705761.post3628651907083980538..comments2023-10-03T04:20:03.184-06:00Comments on Math = Love: Step-by-Step Directions for Factoring Polynomials Using the Box MethodSarah Carter (@mathequalslove)http://www.blogger.com/profile/11839095945000612533noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-1091979517567705761.post-2539458990198332912018-07-12T16:19:10.893-05:002018-07-12T16:19:10.893-05:00I believe that this method fails when there is a c...I believe that this method fails when there is a common factor among all the terms that the students don't recognize. For example, 10x^2 + 80x + 70. If a student didn't recognize that there's a GCF (like many of mine don't), you would multiply 10*70 = 700 and then find two numbers that multiply to 700 and add to 80. This would be 70 and 10. Writing (10x^2 + 70)(x^2 + 10) all over 10.<br />Then you would write it as 10(x^2 + 7)(x^2 + 10) all over ten and leaves (x^2 + 7)(x^2 + 10) as the final answer, which would be incomplete.<br />Am I missing something here?Adinahttps://www.blogger.com/profile/04012807741461325394noreply@blogger.comtag:blogger.com,1999:blog-1091979517567705761.post-65849064211276412232018-03-06T20:43:46.507-06:002018-03-06T20:43:46.507-06:00Do you have anything on factoring 4 terms?Do you have anything on factoring 4 terms?Xochitlhttps://www.blogger.com/profile/10005171030326312050noreply@blogger.comtag:blogger.com,1999:blog-1091979517567705761.post-45808961487926340612017-04-11T19:16:26.410-05:002017-04-11T19:16:26.410-05:00That's even better!That's even better!Anonymoushttps://www.blogger.com/profile/02529950947384580538noreply@blogger.comtag:blogger.com,1999:blog-1091979517567705761.post-41288739442217192382017-04-07T20:26:32.565-05:002017-04-07T20:26:32.565-05:00It's actually not my bed. :) The background ...It's actually not my bed. :) The background is a mouse pad/keyboard pad that sits on my desk at school. Definitely guilty of staying up late blogging, though! Sarahhttps://www.blogger.com/profile/02869398874641834151noreply@blogger.comtag:blogger.com,1999:blog-1091979517567705761.post-2221064345437564882017-04-07T20:24:27.351-05:002017-04-07T20:24:27.351-05:00Love it but I think it's interesting how your ...Love it but I think it's interesting how your pics get closer and closer to what looks like you're bed as you're working more problems. I hope you didn't stay up too late doing this!Anonymoushttps://www.blogger.com/profile/02529950947384580538noreply@blogger.comtag:blogger.com,1999:blog-1091979517567705761.post-3844381762692821012017-04-06T17:09:44.769-05:002017-04-06T17:09:44.769-05:00Another advantage of the harbour bridge method, wh...Another advantage of the harbour bridge method, which I use too, is that you don't need to complete the factorisation if you are finding the zeroes of the quadratic.Anonymoushttps://www.blogger.com/profile/15329687124866666162noreply@blogger.comtag:blogger.com,1999:blog-1091979517567705761.post-68925328900027441722017-03-25T19:48:18.928-06:002017-03-25T19:48:18.928-06:00Thanks so much for this post today Sarah! I am tea...Thanks so much for this post today Sarah! I am teaching factoring this week and this post is SO CLEAR and easy to understand. I love the box method and my students last year really responded to it for multiplying polynomials, but we didn't use it as much for factoring. I am so excited to share it with them this year with my new clarity!Anonymoushttps://www.blogger.com/profile/15555398878346747345noreply@blogger.comtag:blogger.com,1999:blog-1091979517567705761.post-27343931529973362372017-03-25T19:33:52.461-06:002017-03-25T19:33:52.461-06:00LOVE! I start my unit on polynomials and factorin...LOVE! I start my unit on polynomials and factoring this week! This will be so helpful! I have used this in the past, but your explanation and examples are so easy to follow! Can I use your pics in my powerpoint when I teach this?<br /><br />Also, I know it works because I had a student come to me to get some help. I taught him algebra 2 years ago, and he needed help with factoring.....He remembered that we used the box method.Susan Hewetthttps://www.blogger.com/profile/04126108127297053487noreply@blogger.comtag:blogger.com,1999:blog-1091979517567705761.post-27860926374683591402017-03-25T15:12:01.126-06:002017-03-25T15:12:01.126-06:00Well an alternate method to the grid is to use the...Well an alternate method to the grid is to use the harbour bridge method <br /><br />looking at a quadratic ax^2 + bx + c<br /><br />multiply a and c find the factors that add to b<br /><br />so in your example <br /><br />2x^2 + 11x + 5 2 x 5 = 10 factors are 1 + 10 <br /><br />so write it as<br /><br />(2x + 10)(2x + 1)<br />------------------<br /> 2<br /><br />now factor the binomials<br /><br />2(x + 5)(2x + 1)<br />---------------<br /> 2<br /><br />rmove common factors from the numerator and denominator<br /><br />leaving <br /><br />(x + 5)(2x + 1)<br /><br />this method always works... and avoids guess and check.... <br /><br />so looking at <br /><br />15 - x - 6x^2 same process 15 x -6 = -90 <br /><br /> since b = -1 the larger factor is negative -10 and 9<br /><br />(9 - 6x)(10 - 6x)<br />------------------<br /> -6<br /><br />now factor the binomials <br /><br />3( 3 - 2x)(-2)(5 + 3x)<br />----------------------<br /> -6<br /><br />remove common factors and you have (3 - 2x)(5 + 3x) as the solution. <br /><br />Hope it makes sense and gives you another method. <br />(Anonymoushttps://www.blogger.com/profile/13444879580300608011noreply@blogger.comtag:blogger.com,1999:blog-1091979517567705761.post-5023028139099206012017-03-25T09:40:07.004-06:002017-03-25T09:40:07.004-06:00I started using the box method after you first sha...I started using the box method after you first shared it (last year? two years ago?) and I absolutely love it. It was very similar to the way I had taught factoring, but I incorporated it at the same time as multiplying with the box method. It made everything so much more organized and easy to follow. But I love the addition of writing outside the corners what needs to add and what needs to multiply. I had always SAID this, but I never wrote it. Why? No clue. It seems so simple. So thanks for sharing this so I could gather that one more tip. Again, I love boxes!!!Teri Fergusonhttps://www.blogger.com/profile/06490513534041873941noreply@blogger.com