Division of Polynomials made Easy! 1 of 2 - Free Educational videos for Students in K-12

Division of Polynomials made Easy! 1 of 2 - By tecmath

Transcript


00:0-1	you know , Welcome to the Tech Math channel .
00:01	What we're gonna be having a look at this video
00:03	is a way of directly dividing polynomial . Uh So
00:06	it's a really , really great way of dividing polynomial
00:09	. Uh The previous video and most videos you'll ever
00:12	see what you'll R C is a way of doing
00:14	long division of polynomial . But this is a way
00:17	of a shortcut . Okay , this will save you
00:19	lots and lots of work . Um so first off
00:23	I'm gonna write down at the top of polynomial we'll
00:25	be looking at with this . So so we had
00:29	in the last video , by the way we had
00:31	this example here where we went X take away three
00:34	and this was being divided into X squared plus three
00:40	X take away 18 . Okay , so the way
00:46	that we directly divide our Paulino meals is as follows
00:49	, a binomial here into our polynomial is as follows
00:53	. It's really , really simple . A little trickier
00:54	to . It starts out the same way when we
00:56	look at this number here and we basically side this
01:00	number goes into this number . How many times the
01:03	case of X squared divided by X . Is X
01:06	. Okay . Now look , we're starting on their
01:08	way to getting our answer here . There's nothing we're
01:11	going to write down here at all . You're going
01:12	to see this is going to stay fairly clean .
01:15	So what we do now to get our second term
01:17	is we don't write anything down here , we don't
01:19	multiply anything out . What we do is we actually
01:21	look at this minus three here , this negative three
01:24	and we put the inverse to that up here .
01:26	So the inverse of the opposite of -3 is positive
01:30	three . Okay , so now what we're gonna do
01:33	if we're going to get this positive three , we're
01:36	going to multiply by our previous answer and we're going
01:39	to added to this answer here . Okay , then
01:43	You'll see what we do with our answer . It's
01:45	a fairly fairly common sense sort of thing . So
01:48	positive three Times X is three x Plus three X
01:53	. is six x . Okay . So I'm gonna
01:55	put the six down here , but what you're gonna
01:58	see is we've already got our backs here , so
02:00	we're actually gonna divide , we're actually not going to
02:02	put that X down here , we're gonna just forget
02:04	about it for a minute because we're going to exhale
02:07	. So the next answer is going to be without
02:09	an X or X . The parents zero . So
02:11	this just becomes positive six . That is there a
02:16	heads up ? Okay , wait a second . You
02:18	say ? Surely that can't be it ? It is
02:21	. Wait a second . I think you probably need
02:23	to go through another one of these to see how
02:24	simple this actually is . So all right , the
02:29	next question down . So so we have this one
02:33	this will take a little bit of getting used to
02:35	. So don't just look at that last one and
02:37	say I don't get that at all , I'm never
02:39	gonna be able to do this . So we're gonna
02:42	divide X -500 x . four eggs are a pair
02:47	of four . Take away X to the power of
02:49	three . Uh Boris 21 x squared . What about
02:58	we do ? Plus 11 X . We will go
03:04	plus Take by 32 . Okay , now what we're
03:10	gonna do with this is we're going to get this
03:12	equation and we're going to directly divide it . So
03:15	first off , I'm just going to move it across
03:17	, so it's a bit more center . There we
03:19	go . And we're gonna divide this directly . So
03:21	we're not gonna get any of this working down here
03:23	. So first off , we look at our terms
03:25	here and we say X goes X to the power
03:29	of four . How many times it goes in X
03:32	to the three times ? So the next dance is
03:34	going to be an X squared answer . The next
03:37	one is going to be an X to the power
03:38	of one , answer . The next power is going
03:40	to have no X . And then this will just
03:42	be a reminder part down here . How do you
03:44	get that ? So first off , we look at
03:47	this to get our next part , we look at
03:49	the inverse of this -5 , which is positive five
03:51	positive five . We both applied upon this study here
03:55	and we added to the next time . Okay ,
03:58	so positive five cards , X cube Is positive five
04:05	x Cube . We're going to add it to this
04:08	study here which is body executes . We're gonna end
04:11	up with four X . We're not gonna put down
04:13	four x cubed . We go the next power down
04:17	which is squared . Okay so that's a positive .
04:23	Okay so to get the next part of our answer
04:25	, you're gonna see it's going to be not X
04:26	squared . It's going to be an X . Okay
04:29	. The next pair of one so Positive five times
04:33	4 x squared is 20 X squared minus 21 X
04:38	squared . His bought us pigs . Okay about this
04:43	one x But not square . This is going to
04:48	be the power of itself . Power of one .
04:51	Okay . So we get to the next part of
04:53	our answer . Five times minus X . Is minus
04:59	five X plus 11 X . Is positive six .
05:04	Okay don't positive six x . Because by times minus
05:09	X is minus five X plus 11 X is positive
05:13	six X . We're not gonna put that six down
05:14	here with that accent is going to put the six
05:16	down . Okay you're pretty good with this . So
05:21	then we now have a look into what we have
05:23	left . So the way we do this is as
05:24	follows we go five todd six which was 30 .
05:30	We're going to add this to this , so 30
05:33	plus minus 32 is minus two so we've a remainder
05:36	was minus two . Isn't that pathetic ? And the
05:39	easiest way of doing this rather than having all this
05:42	working out which you would have seen on this other
05:44	video I made or other people's videos . This is
05:47	a direct way of doing this and it works .
05:50	Okay . So what about we have a look at
05:52	another example . How does that sound ? Uh So
05:55	okay we'll do one which is now let's let's do
05:59	it equally as big , I'll get rid of all
06:02	these and we will work this one out . Okay
06:07	, so what about we do expose to that ?
06:12	We're gonna divide that into two X two , the
06:18	fires plus six X to the fore . Now this
06:22	one is going to be utterly enormous , isn't it
06:24	? Plus seven X to the three plus X squared
06:32	uh minus 13 X uh minus 16 . Look at
06:38	that , I run out of line , they're better
06:41	extend that . So let's directly divide this in now
06:45	. So first off , what we do is we
06:48	look how many times is X going to two X
06:51	the five and you're going to see that it goes
06:53	in two X . Our of four and that's our
06:59	first term . So the next one is going to
07:01	be next to the power of three , next to
07:03	the power of to the next to the power of
07:04	one . Uh Just a normal term . So yeah
07:09	, inverse of positive too . It's negative too .
07:12	So by this too , Times two Extra 4 .
07:16	Yes -4 X to the fore . We're gonna add
07:21	that to six X to the fourth . So we're
07:22	gonna get to exit before but it's something to positive
07:25	two X before we go down the power . So
07:27	it's gonna be two X to the power of three
07:32	. Okay , so we get the next term ,
07:33	we're going to go -2 times positive too , which
07:38	is By this four X to the power of three
07:43	. We're going to add this to seven X to
07:44	the power of three , so minus four plus seven
07:47	is positive three X to the power . Not a
07:52	three though , we're going to put it down to
07:53	the power down so X squared . Okay , next
07:57	we're gonna go minus two times three X squared minus
08:00	six X squared plus X squared is going to be
08:05	minus five X squared because minus six plus one is
08:09	minus five . Okay , so minus five not X
08:12	squared It's just gonna be X . Okay minus two
08:16	times minus five is minus two times minus five X
08:20	. Sorry , is uh minus 10 is positive 10
08:24	X . It's a positive 10 X plus 13 X
08:28	is -3 Because we're gonna go the next power down
08:33	. Okay ? So we're not going to have any
08:35	extra at all . What's the remainder going to be
08:37	? Well , it's going to be minus two times
08:39	minus three , which is six plus six days .
08:43	So a reminder , it's too it calls that right
08:48	? That is a really , really fast way of
08:50	doing it . Now . In the next video ,
08:51	I'm gonna show you what to do when we deal
08:54	. Say I put a two here , Okay ,
08:57	because there's a slight little trick that we have to
08:58	do , I hope to see that . Okay ,
09:00	bye .

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Division of Polynomials made Easy! 1 of 2 is a free educational video by tecmath.

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