Algebra Math Trick - Division - By tecmath
Transcript
| 00:00 | Good day , Welcome to Tech Math channel . What | |
| 00:02 | we're going to be having a look at this video | |
| 00:04 | is this is the second video . Look at the | |
| 00:05 | direct division of polynomial . And this is a great | |
| 00:09 | little direct division trick rather than having to worry about | |
| 00:11 | a long division that typically occurs with polynomial . Okay | |
| 00:15 | , so if you haven't seen the first video looking | |
| 00:18 | at this trick , I recommend you have a look | |
| 00:19 | because this is a bit of an extension of that | |
| 00:21 | trick . So I'm going to launch into right now | |
| 00:24 | the next part . So we have uh , so | |
| 00:29 | we have this sort of problem two X plus two | |
| 00:32 | . We're going to be divided this into the following | |
| 00:38 | eight X cubed plus 12 X squared . What is | |
| 00:46 | two x Plus 1 ? Now , if you've already | |
| 00:50 | seen that previous video , maybe you give this a | |
| 00:53 | go . But you're going to notice the difference here | |
| 00:55 | is we have this coefficient here , which is to | |
| 00:58 | and this has to be taken into account . So | |
| 01:01 | I want to start out , maybe give this a | |
| 01:03 | go , you pause the video you want to go | |
| 01:04 | . But I'm gonna start the explanation of how you | |
| 01:06 | can directly divide this sort of term into this world | |
| 01:10 | . And this is how so what we do is | |
| 01:13 | the following . We look at our first terms here | |
| 01:15 | eight X cubed and two X . And we say | |
| 01:18 | how many times two X . Going to eight X | |
| 01:20 | cube ? And it goes in to goes into 84 | |
| 01:24 | times and X goes X cubed X square times . | |
| 01:31 | Okay , so it's the first answer . What we're | |
| 01:34 | doing with a trick before or their directive division is | |
| 01:38 | we were working at an inverse of this number here | |
| 01:41 | , which is -2 to get our second term , | |
| 01:44 | but I'm going to add this one little thing as | |
| 01:46 | well . And this is the idea of a divided | |
| 01:48 | Okay , you gotta look at this number here . | |
| 01:51 | So before we were doing this we're getting this number | |
| 01:53 | , we're multiplying it by this number . We're adding | |
| 01:55 | into this number and this is giving us our answer | |
| 01:57 | here . But we have an extra step because this | |
| 02:00 | two X and it is this what we have to | |
| 02:02 | do is we have to divide by this coefficient . | |
| 02:05 | So the answer we get we're going to divide by | |
| 02:08 | two . Okay , this is a three X . | |
| 02:10 | We divide by three . So we'll work through this | |
| 02:13 | and you'll get used to this . So it's pretty | |
| 02:16 | simple . So minus two times four X squared is | |
| 02:20 | eight X squared plus 12 weeks squared . So minus | |
| 02:25 | eight X squared plus 12 X squared . Minor site | |
| 02:28 | Plus 12 is positive four . But we're gonna divide | |
| 02:35 | our answer by two . So positive two X squared | |
| 02:39 | , divide a positive four X squared , divided by | |
| 02:41 | two is positive too . Ex yeah . The other | |
| 02:46 | thing which you might remember from the other video Yes | |
| 02:48 | we don't put down X squared we go the next | |
| 02:50 | power down so it becomes positive two X . Okay | |
| 02:54 | which makes sense . Okay because this is X squared | |
| 02:56 | this is going to be exhale . So let's get | |
| 03:00 | the next part of our answer . So minus two | |
| 03:04 | times two X . Is minus four . X -4 | |
| 03:08 | x -2 x 66 So it's nothing to be minus | |
| 03:13 | six to minus six . And we can divide our | |
| 03:16 | answer by two . So minus six divided by two | |
| 03:19 | . His borders three . Okay let's see now about | |
| 03:25 | if there's a reminder . So -2 times -3 -2 | |
| 03:31 | times -3 is six . So six plus 1 is | |
| 03:37 | seven and you don't need to divide the coefficient into | |
| 03:39 | this . A remainder is seven so that's the way | |
| 03:43 | we get the answer there . Okay , I reckon | |
| 03:45 | you might be a little bit confused by this . | |
| 03:47 | So I'm going to go through a couple more examples | |
| 03:50 | with this . Okay , So take your time working | |
| 03:52 | out and we'll save you a lot of . All | |
| 03:55 | right , a lot of workings out . Okay . | |
| 03:58 | Especially we've already started doing long division of polynomial because | |
| 04:01 | you realize that that's quite a big thing . So | |
| 04:06 | What about we get three x . Take a way | |
| 04:10 | forward and we're going to divide this . It's annoyed | |
| 04:18 | Extra pair of four by the six X to the | |
| 04:21 | power of three Uh plus 17 squared minus 11 X | |
| 04:33 | ball is 12 . Okay ? And if you really | |
| 04:36 | think you're up to it , you might actually even | |
| 04:37 | pause the video and trying to give this one to | |
| 04:39 | go . There's gonna be another example after this . | |
| 04:41 | Okay , so the way we do this again is | |
| 04:44 | as follows . So we look here and we say | |
| 04:47 | three x goes into nine X . To the power | |
| 04:50 | of 49 goes into 33 goes into nine sorry three | |
| 04:55 | times and X goes into extra power of four X | |
| 04:59 | to the power of three times . To an extent | |
| 05:00 | is gonna be next square the one after is gonna | |
| 05:02 | be an X . Okay so it's gonna be that | |
| 05:04 | power down each time . Okay so the inverse of | |
| 05:10 | this negative for its positive for and we're gonna be | |
| 05:14 | dividing by this coefficient here which is going to be | |
| 05:16 | a dividing by . That's right okay so let's get | |
| 05:22 | our second term positive for Todd's three x cubed is | |
| 05:27 | 12 x cubed 12 x cubed . Take away six | |
| 05:30 | x cubed is six x cube divided by three is | |
| 05:37 | To execute . We're not going to have to execute | |
| 05:39 | we're gonna go to power down so it's going to | |
| 05:40 | be plus two eggs squid . Okay lets go the | |
| 05:49 | next part of areas positive for times two X squared | |
| 05:53 | is positive . Eight X squared positive . Id X | |
| 05:58 | squared . Okay so eight X squared plus 17 squared | |
| 06:03 | is 15 X squared 15 X squared . So we're | |
| 06:06 | going to go to power down which is 15 X | |
| 06:09 | divided by three . is 15 x divided by three | |
| 06:15 | is positive . Five X . Okay . The next | |
| 06:21 | part of our answer positive for times five X . | |
| 06:25 | Is positive . 20 X positive . 20 X . | |
| 06:28 | Takeaway 11 X . Nine X nine X . To | |
| 06:32 | the power now which is gonna be 99 divided by | |
| 06:34 | three is 32 plus three . And we can see | |
| 06:41 | if we have a reminder for Times three is 12 | |
| 06:47 | . This 12 is going to counsel at this 12 | |
| 06:49 | so we don't have any reminder at all . Okay | |
| 06:54 | So how did you go with that ? What about | |
| 06:56 | one more example ? Okay sorry Let's do uh example | |
| 07:09 | here we're gonna do four x minus two . We're | |
| 07:14 | going to divide this into uh eight X . The | |
| 07:22 | power of three minus 36 X . to the power | |
| 07:28 | of two plus 12 X plus four . Okay . | |
| 07:35 | Now , first off , you might look at this | |
| 07:38 | and you might give this a go before I haven't | |
| 07:40 | . You better go so you might pause it can | |
| 07:42 | go but I'm gonna start working through it right now | |
| 07:45 | . So first off , four X goes into eight | |
| 07:47 | X cube four goes into 82 times and X goes | |
| 07:50 | into X cube X squared times . We're gonna be | |
| 07:54 | starting with the squared OK , So we have a | |
| 07:57 | positive to here because it's the universe of that and | |
| 07:59 | uh coefficient is four . So we're gonna be dividing | |
| 08:02 | your answer by four . Okay , so two times | |
| 08:07 | two X squared is four X squared . Take away | |
| 08:10 | 30 60 X . 36 X squared is 32 X | |
| 08:15 | squared . So I want to go to power down | |
| 08:17 | which is 32 X . And 32 divided by four | |
| 08:21 | , x divided by four years . Right . X | |
| 08:26 | . Is this a positive or a negative ? It's | |
| 08:28 | going to be a negative . Okay , just be | |
| 08:31 | really , really careful that because with this , you | |
| 08:35 | know , we're going to times two is 44 from | |
| 08:38 | 36 minus 36 is a positive four plus four plus | |
| 08:44 | minus 36 is third minus 32 . So where the | |
| 08:46 | minuses there ? Okay , so too times eight X | |
| 08:51 | is going to be 60 negative 16 X negative 16 | |
| 08:55 | X plus 12 X is going to be minus four | |
| 09:00 | x minus four X . So I'm going to get | |
| 09:03 | that power off so minus four divided by four is | |
| 09:06 | minus one . So let's see if there was a | |
| 09:10 | reminder here . So to times minus one minus two | |
| 09:15 | minus 24 minus two , we're gonna end up with | |
| 09:19 | the remainder uh two for minus two is two . | |
| 09:22 | So isn't that a really , really cool method ? | |
| 09:24 | I hope you like that ? Uh Putting comments say | |
| 09:26 | I don't understand it all , I put in comments | |
| 09:28 | saying I really , really like it . Uh I'm | |
| 09:30 | happy either way . Anyway . Hopefully . Yeah , | |
| 09:33 | that helped you out , see you next time . |
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Algebra Math Trick - Division is a free educational video by tecmath.
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