Long Division of Polynomials - Free Educational videos for Students in K-12

Long Division of Polynomials - By tecmath

Transcript


00:0-1	today . Welcome to the Tech Math channel . What
00:02	we're going to be having a look at this video
00:03	is a long division of polynomial . Okay , so
00:06	it's a way of dividing polynomial um using long division
00:10	And this is going to lead us then to looking
00:12	at a direct way of dividing polynomial is Ok .
00:15	A bit of a trick for a faster way of
00:17	dividing polynomial . Okay . We're gonna start out with
00:19	the standard way that we're going to move to the
00:21	a lot faster way . So an example of how
00:25	to divide polynomial is an example of where this would
00:27	look like a question like this . We would look
00:28	like this say X squared . Uh We're going to
00:32	add three X and we're going to take away 18
00:36	and into this we're going to divide Ux x take
00:41	three . So first off , we're going to do
00:44	the long division of these . It's really , really
00:46	important that we rewrite this . Okay , so it
00:49	looks like a long division question . So the way
00:51	that we do this is as follows , I'm going
00:53	to get this X squared plus three X . Take
00:59	away I . D . Uh I'm going to write
01:02	this like a division question , I'll get rid of
01:05	that . It's not a very good mind and I
01:07	write this like a division question . Okay , so
01:10	what we have is X take away three . Okay
01:15	, I'm going to get rid of this first part
01:18	now because it's a little bit a bit clunky I
01:20	think . So let's get rid of that and we'll
01:24	move this so it's in the center here . So
01:29	we're going to divide this particular equation here now to
01:33	do this , we do the following actually , before
01:36	we do , I think it's really , really important
01:37	to know . Just something to make sure of ,
01:39	make sure that your powers here are in descending order
01:42	. So we're gonna get the odd questions tricky question
01:45	where you're going to have to reorder them look 99%
01:48	of the questions are going to be like this where
01:49	you have X squared X X to that , you
01:52	know zero . But just make sure this is the
01:55	case . Okay , so that's a really important step
01:59	by the way . So first off the way that
02:01	we divide this is we look at our numbers here
02:03	, we have X squared and we have X .
02:06	So we look at these first numbers here were the
02:07	first variables here and we say , what do we
02:11	need to multiply by X here to get X squared
02:13	or how many times X go into X squared here
02:16	and the answer to that is exit goes X times
02:20	X times X , Z X squared . Now what
02:24	we do is we have to take this off our
02:27	number here . So what we do is we go
02:31	X times X is X squared and X times minus
02:36	three is minus three X . And we're going to
02:40	put these in brackets were apparent thesis as you might
02:42	call them and I'll probably mispronounce that and we're going
02:46	to take that away . So let's do that .
02:49	So X squared takeaway X squared , you're going to
02:51	find these guys cancel each other out . Then you're
02:53	gonna look at this term here and you're gonna have
02:56	three X . And we're gonna take away minus three
02:59	X three X . Takeaway minus three X . Well
03:03	minus minus is the same as placing . So answer
03:06	here Is going to be six x . And we
03:09	just bring this term down which is modest items .
03:14	Okay , So we get to the next part of
03:16	our question which is this one we have six X
03:20	. Take away and that's what we have left .
03:22	And we're still trying to divide this X take away
03:24	three . And so we look at our numbers down
03:26	we say what goes into both what with Xia and
03:31	six X . Basically how he told his ex going
03:34	to six X . And the answer is it goes
03:36	in six times Okay ? It goes in positive six
03:41	times . Okay . So now what we do is
03:43	the same sort of thing six times x . There's
03:47	six X . So they're going to cancel it one
03:49	. You probably work that out already and six Tops
03:53	-3 is by this 80 . Okay . And we're
03:57	going to take this away . So these two cancel
04:02	each other out then minus 18 minus minus 18 .
04:05	Well minus and minus becomes a plus 18 plus 18
04:08	. These guys also cancel each other out . So
04:11	our equation is finished . Our answer is X squared
04:15	plus three X minus 80 divided by X . Take
04:18	away through Is X-plus six . So hopefully you get
04:22	this . Okay now we're gonna go through one more
04:24	example of the long division here just to see how
04:27	you go . So I'll rub this one out and
04:32	I think I'll put a bit of a harder example
04:34	here . I'll do for example this one here .
04:40	Say we do . I'm going to write it in
04:43	a good way straight away . So so we are
04:47	too . This is the number is going to be
04:49	divided by two X plus two and I'm going to
04:52	be dividing that into ID X cubed Plus 12 weeks
05:00	squared Boris two X plus one . Okay , so
05:10	we're going to do this using long division now .
05:12	First off , our powers are all in order so
05:15	everything's cool . We can start just doing this .
05:16	So what number looking at these numbers here are eight
05:19	X cube and our two X . What number do
05:21	we how many times two X . Going to execute
05:25	the answer to that is it goes in 4 2
05:28	goes into 84 times and X squared . Okay .
05:34	Because X and X cubed goes X square todd .
05:37	So now we're gonna multiply these out . So we
05:39	got four X squared times two X his I'd execute
05:46	and this is going to be added to two times
05:50	four X squared , which is going to be I
05:55	X squared . Okay , put these in brackets very
06:00	apparent thesis will take them away and we're going to
06:03	get the following we're going to end up with eight
06:08	X cubed . Take away an excuse to cancel one
06:10	another out . So 12 X cube take away eight
06:13	xQ eight X squared , Sorry , 12 weeks square
06:16	take away Eight X squared is going to be four
06:19	X squared . And these numbers were just going to
06:22	carry down . Okay , so we're gonna end up
06:25	with -2 x plus word . Okay , What we
06:30	do now is we look at what's over here and
06:34	what number here so many times it's two X .
06:36	Go into four X squared . It goes into how
06:38	many times the two goes into four positive two times
06:43	and X goes to the X squared extorts . Okay
06:48	, so let's multiply this out again to X times
06:52	two X is for X squared . They're gonna cancel
06:56	one another out . And their two x times positive
07:00	too is positive for eggs . Okay ? We're going
07:07	to take that A . Y . Okay , so
07:11	four take away for these guys are going to council
07:15	one another out . Okay . And that minus two
07:18	X . Takeaway positive for so minus to take a
07:22	positive for is minus six X . So you can
07:26	actually write a different colour I think . So we
07:28	write this down , we write this in black dancing
07:32	, so this is going to be minus six X
07:38	. Okay this one Positive one is also gonna be
07:41	carried in . Okay , so we're almost finished .
07:46	We need to look at disturber And this number how
07:49	many times it's two x . Going to -6 X
07:54	. He goes in negative straight times . Okay ,
07:58	so do the same thing minus threatens uh minus three
08:04	times two X six X . Well by the six
08:08	x . And Monastery Times two Is -6 . So
08:15	we're gonna put these in brackets , we're gonna take
08:16	it away By six . Take away -6 . Takeaway
08:21	-6 is going to be the same as minus six
08:25	plus six X . Sorry . And we're going to
08:27	get the answer is zero and positive won't take away
08:32	minus six is the same as positive one plus six
08:35	. So we're going to get the answer of seven
08:38	. Okay ? So this seven is going to be
08:41	a reminder reminder of seven . Okay because we can't
08:45	divide two X plus 2 to 7 we've got a
08:49	remainder . So that's our answer . Now the link
08:51	I want to put up now is going to show
08:53	you a way of pretty much eradicating all of these
08:57	steps and pretty much just going straight to your answer
09:01	here . So I really recommend you check it out
09:04	if you want to save yourself a fair bit of
09:06	time I'll see you then . Bye .

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