tag:blogger.com,1999:blog-10348701.post3359456603592649312..comments2021-07-22T20:06:55.614-07:00Comments on Right on the Left Coast: Views From a Conservative Teacher: So Smart They're Dumb?Darrenhttp://www.blogger.com/profile/15730642770935985796noreply@blogger.comBlogger17125tag:blogger.com,1999:blog-10348701.post-38660742949426867812014-09-29T01:35:12.273-07:002014-09-29T01:35:12.273-07:00Because you CAN divide both sides by 3 ... because...Because you CAN divide both sides by 3 ... because 3 can't be zero. So it can be appealing to try the same thing with x ...maxutilshttps://www.blogger.com/profile/11294262473781967372noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-36922005187732685312014-09-28T21:18:52.396-07:002014-09-28T21:18:52.396-07:00There's also the simple check that should be o...There's also the simple check that should be one of the first things a person thinks about: a 3rd power polynomial likely has 3 roots.Auntie Annhttps://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-29672993189738954532014-09-28T12:14:12.820-07:002014-09-28T12:14:12.820-07:00"Dividing both sides by x without checking to..."Dividing both sides by x without checking to see if 0 is a possible solution ... I can't even imagine doing that."<br /><br />I don't understand the thinking/mistake behind dividing both sides by x at all. You've got the equation in a form with all the xs on one side and the other side equal to zero. This is what you want, right?<br /><br />What sort of mistaken idea would lead you to divide by x here (rather than factoring out the x)?<br /><br />-Mark RouloAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10348701.post-17371640035539245852014-09-28T04:18:37.277-07:002014-09-28T04:18:37.277-07:00Auntie Ann ... that's the beauty of factoring ...Auntie Ann ... that's the beauty of factoring ... you don't have to remember that rule. It presents itself to you... it also means you don't have to check for 0 being an answer, because it is also right there. Dividing both sides by x without checking to see if 0 is a possible solution ... I can't even imagine doing that.<br />maxutilshttps://www.blogger.com/profile/11294262473781967372noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-5144063061740307012014-09-27T18:58:01.332-07:002014-09-27T18:58:01.332-07:00I could easily see not getting the + or - part. Th...I could easily see not getting the + or - part. That's easy to forget.Auntie Annhttps://www.blogger.com/profile/05777983027361603449noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-2718214522436573122014-09-27T18:13:55.786-07:002014-09-27T18:13:55.786-07:00Leave it to me not to come up with the worst metho...Leave it to me not to come up with the worst method ... :)<br />Anoymous -- no need for the quadratic on (x^2-3) ... it factors easily to (x + rt3)(x- rt3)...maxutilshttps://www.blogger.com/profile/11294262473781967372noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-65110812105671939542014-09-27T16:57:41.364-07:002014-09-27T16:57:41.364-07:00The most common incorrect answer was to add 9x to ...The most common incorrect answer was to add 9x to both sides and, when dividing both sides by x, forget the stipulation about checking if x=0 is a solution.<br /><br />Of course the "best" way to solve it would be to factor a 3x out of the left side, leaving 0 and +/-root three as solutions.Darrenhttps://www.blogger.com/profile/15730642770935985796noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-5740644028196628592014-09-27T11:17:09.470-07:002014-09-27T11:17:09.470-07:003x^3 - 9x = 0
3x (x^2 - 3) = 0
3x (quadrtratic e...3x^3 - 9x = 0<br /><br />3x (x^2 - 3) = 0<br /><br />3x (quadrtratic equation goes here) = 0, or<br />x = 0; sqrt(3); -sqrt(3)<br /><br />Did they miss the negative solution to sqrt(3) ?<br /><br />-Mark RouloAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10348701.post-14236172273214943612014-09-27T11:10:04.734-07:002014-09-27T11:10:04.734-07:00Not eyeballing it to see if x=0 worked? Ie, not t...Not eyeballing it to see if x=0 worked? Ie, not thinking about what they were doing.<br /><br />-Mark RouloAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-10348701.post-38009291655967064132014-09-27T08:45:32.279-07:002014-09-27T08:45:32.279-07:00will you post the answer later? will you post the answer later? Teacher gardenerhttps://www.blogger.com/profile/13208175008287749994noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-56168242807341687932014-09-27T08:43:11.741-07:002014-09-27T08:43:11.741-07:00They did this:
3x^3=9x
3x^2=9
x^2=3
x=sqrt(3)
Th...They did this:<br /><br />3x^3=9x<br />3x^2=9<br />x^2=3<br />x=sqrt(3)<br /><br />They certainly missed the zero solution, and probably half of them missed -sqrt(3). (Yes, I work with HS students)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10348701.post-30100738303889178982014-09-27T08:14:30.145-07:002014-09-27T08:14:30.145-07:00Rather, I've seen this approach taken with tri...Rather, I've seen this approach taken with trinomials that DO have a middle term ~<br /><br />gotta love typos ~sdsdfdhttps://www.blogger.com/profile/07105751880532308204noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-75023360312528931512014-09-27T08:10:25.879-07:002014-09-27T08:10:25.879-07:00Let's see - putting on my "typical studen...Let's see - putting on my "typical student" hat, I'll take a stab:<br /><br />* Subtract 9x from both sides<br />* Divide both sides by 3<br />* Take the cube root of both sides<br /><br />Answer: x = cube root of x<br /><br />What could be simpler ;) ?<br /><br />(I've seen this essential approach taken with quadratic trinomials that don't have a middle term, so I'm guessing they could utilize the same rationale with a cubic that has no middle terms ~ )sdsdfdhttps://www.blogger.com/profile/07105751880532308204noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-37033102027018843532014-09-27T04:49:00.755-07:002014-09-27T04:49:00.755-07:00not using 0 as a solution?
not using 0 as a solution?<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-10348701.post-66994239033725910862014-09-27T00:05:34.902-07:002014-09-27T00:05:34.902-07:003x(x^2 - 3)
x = 0; x = sqrt 3; x = -sqrt 3 ... so...3x(x^2 - 3)<br /><br />x = 0; x = sqrt 3; x = -sqrt 3 ... so, I dunno.<br /><br />I'm guessing they added 9x to both sides, then divided the x out ...?PeggyUnoreply@blogger.comtag:blogger.com,1999:blog-10348701.post-37738096723622016032014-09-26T22:29:08.646-07:002014-09-26T22:29:08.646-07:00And more specifically, now that I looked at it mor...And more specifically, now that I looked at it more closely, not being able to recognize the difference of two squares.maxutilshttps://www.blogger.com/profile/11294262473781967372noreply@blogger.comtag:blogger.com,1999:blog-10348701.post-69265896157115447452014-09-26T22:27:54.093-07:002014-09-26T22:27:54.093-07:00No question. Not being able to factor.No question. Not being able to factor.maxutilshttps://www.blogger.com/profile/11294262473781967372noreply@blogger.com