SAT Math Part 19 - Long Division of Polynomials - Free Educational videos for Students in K-12

SAT Math Part 19 - Long Division of Polynomials - By The Organic Chemistry Tutor

Transcript


00:00	number 69 . Which of the following answer choices is
00:05	equivalent to the expression shown below . So we have
00:10	12 x squared -8 x plus 15 Divided by two
00:15	. Ex Monastery . Is that equivalent to answer choice
00:19	A . BC . D . or which 1 ?
00:24	Now there's two ways in which we can get the
00:26	answer . We could use long division or we can
00:30	plug in numbers . Let's try plugging in numbers .
00:34	Let's plug in tune into the expression . So this
00:39	is going to be 12 times two squared minus eight
00:43	times two plus 15 on the bottom . It's going
00:47	to be two times to monastery two squared is four
00:52	, eight times 2 is 16 . two times 2
00:56	is four and 12 times four is 48 negative 16
01:02	plus 15 is negative one . four . Monastery is
01:05	one . So this whole thing is 47 when access
01:10	to Yeah . Yeah . Now let's see which answer
01:20	choice is equal to the same thing . Let's start
01:23	with a six times 2 -4 . That's gonna be
01:28	12 -4 which is eight . So that's not 47
01:32	. We could eliminate as a choice A . Mhm
01:37	. Now let's repeat the process with answer choice B
01:42	. six times 2 is 12 . 12 -5 is
01:46	seven . So that's not 47 . Yeah . Now
01:51	let's try answer choice C . Yeah so it's six
01:55	times two plus five plus 30 over two X .
02:01	Monastery or two times to monastery . six times 2
02:05	is 12 . Two times two is four . Monastery
02:10	. That's one . 12 plus five is 17 17
02:15	plus 30 is 47 . So the correct answer for
02:20	this problem is answer choice C . So that's one
02:24	way in which you could solve these types of problems
02:28	. It's by plugging in numbers but let's use long
02:33	division to confirm our answer . Yeah So let's set
02:38	it up this way I might need more space .
02:50	So here's the process for long division Step one divide
02:54	step to multiply step three subtract . So let's divide
03:00	12 X squared by two X . Yeah , That's
03:03	going to give us six x . Next multiply six
03:08	X times two X . Is 12 X squared .
03:12	Yeah . Six X times negative three is negative 18
03:15	X . So now we need to subtract 12 X
03:20	squared minus 12 X squared . That's going to be
03:23	zero . They're going to cancel negative eight minus negative
03:29	18 . That's negative A plus 18 . So that's
03:33	going to be positive tent And a 15 . We
03:36	could bring it down . Now let's repeat the process
03:42	. So let's divide 10 x by two x .
03:46	10 x divided by two XS 5 . Next let's
03:50	put our subtraction symbol and then multiply five times two
03:57	X . Is 10 X . Five times negative three
04:03	. That's going to be negative 15 . Now let's
04:06	subtract 10 -10 x . is zero 15 -20 .
04:15	The two negative signs will become a positive sign .
04:18	So that's 15 plus 15 which is 30 . Now
04:23	, the way you write your answer will be like
04:25	this . So what we have here , all of
04:28	this is equal to what we see here on top
04:33	. That's six x plus five plus the remainder ,
04:39	which is 30 Divided by what you try to divide
04:44	it by , which is two x monastery . So
04:47	that's how you can get the final answer , which
04:50	is an citrusy number 70 . If our fx which
04:56	is equal to two X cubed minus seven X squared
05:00	-18 x plus 63 and sfx is equal to x
05:06	squared minus two X minus 15 . Which of the
05:11	following expressions is equivalent to r f X divided by
05:15	sfx . So let's divide those two first , so
05:22	are divided by S Our is two XQ seven X
05:28	squared in . You know what the best is ?
05:31	Yeah and S is X squared minus two X minus
05:38	15 . So what do you think we need to
05:40	do here looking at our answer choices , We can
05:47	see that we may have to use long division ,
05:52	but it's wise if we factor first before using long
05:56	division now , you could plug in numbers so you
05:59	can try that technique if you want to you can
06:02	even do so now , but that's going to be
06:04	a lot of work , especially if the answer is
06:09	not in the beginning . So let's begin by factoring
06:14	the numerator . It looks like we can factor by
06:18	grouping -7 divided by two is the same as 63
06:23	, divided by -18 . So let's take out the
06:28	G c f in the first two terms . So
06:31	that is going to be x squared two X cubed
06:35	divided by x squared is two X negative seven .
06:39	X squared divided by x squared is just negative seven
06:44	. Now let's do the same thing for the last
06:46	two terms . So we could take out a positive
06:50	nine . Actually no , a negative time negative 18
06:55	X divided by negative nine is two X 63 divided
07:00	by -9 is negative seven . So now let's factor
07:06	out two X -7 . If we do , we're
07:08	going to have x squared and negative and I now
07:16	we can factor x squared minus line . Using this
07:19	formula A square minus B squared is a plus B
07:24	times A . Might this be so A is going
07:33	to be X B is the square root of nine
07:37	which is street . So X squared minus nine .
07:39	Can be factored two x plus three x monastery .
07:47	I'm going to write everything on the right side so
07:51	far . This is what we have for the numerator
07:53	To access -7 Times X-plus three times X minus tree
08:00	. Yeah . Yeah . Okay , now let's focus
08:07	on factor in this . Try no meal . How
08:10	can we do ? So first we need to numbers
08:15	that Multiplied to -15 But add to -2 . So
08:22	this is going to be five and 3 , but
08:24	particularly negative five , positive three , negative five plus
08:29	three adds up to negative two . So we can
08:33	write this size X -5 times x plus three .
08:37	Yeah . Yeah . So at this point we could
08:43	simplify , we could cancel the factor X plus tree
08:49	. So we have two X -7 Times x monastery
08:55	over X -5 . Now this doesn't look like any
09:00	of the answer choices up to this point . So
09:04	we still have some more work to do . Yeah
09:07	. So what we're going to do now is we're
09:10	gonna foil . Let's multiply these two binomial . So
09:17	we have two x . times x . That's two
09:21	x squared two X . Times negative three . That's
09:25	negative six X . And then combine that with -7
09:29	X . That's negative 13 acts Next -7 times -3
09:37	. That's plus 21 Divided by X -5 . So
09:44	what we're gonna do now is we're going to use
09:45	long division . So let's divide first two X squared
10:01	divided by X . Is two X . Now let's
10:06	put our subtraction symbol and multiply two x divided by
10:11	X . I mean multiplied by X . Is two
10:15	X squared . And then two x times negative five
10:19	. That's gonna be negative 10 x . So now
10:23	we're gonna subtract these will cancel and then we have
10:26	negative 13 X minus negative 10 X . So that's
10:31	negative 13 X plus 10 X . Which is -3
10:35	acts . Let's bring this down . And then we're
10:38	going to divide yeah negative three X . Divided by
10:42	X . Is negative three and then multiply negative three
10:49	times X . Is negative three X -3 times negative
10:53	five is positive 15 . Mhm . So we have
10:59	21 -15 which is six . Yeah . So this
11:05	fraction can be written as two x . modest tree
11:10	Plus the remainder six Divided by X -5 . Yeah
11:17	. So this right here is the final answer answer
11:20	choice D .

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