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TSI Math: Factoring a Multivariable Trinomial 3 Views


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Description:

Factor completely.
3x² + 4xy – 4y²


Transcript

00:03

Okay sy mash bumpers Next up Two words for you

00:07

Factor completely That's beef flank The new james bond movie

00:13

titles So let's just dive right in Well there are

00:16

legends about its existence stories of unicorns dragons But nothing

00:20

is prepared us for the sighting of a creature as

00:22

elusive as the multi variant Try no meal That's what

00:25

that thing is face the ferocious creature by attacking the

00:28

variables first Well the x squared the y squared terms

00:31

break into their individual factors of x times x and

00:34

white times Why Pretty easily there right Well placing the

00:37

variables in the first and last terms And each binomial

00:39

naturally creates the x y term in the middle of

00:42

the tri no meal while unlike the heads of the

00:44

infamous greek hydra the regrown variables of this flavour Good

00:48

Okay last term is negative so that by no meals

00:51

must have opposite signs Okay so see this is minus

00:55

and that's a plus thinking Yeah well the coefficients of

00:57

the tri no meal or handled as usual The first

00:59

coefficient is a prime and has only two factors One

01:02

and three in the last coefficient for their has factor

01:04

Pairs of one and four in two and two Right

01:06

Well start With little trial and error to find the

01:08

right combo here nobody gets this right off the bat

01:11

usually and let's try on all three Acts and money's

01:14

4 times x plus y is that work Well Is

01:16

the proposed factor pair valiant enough to pass the first

01:19

trial Well it's multiply the binomial tze and find out

01:22

so we got three exponents for why'd times x plus

01:25

y so inside and an outside then we had the

01:27

middle Remember how all that works so let's Think about

01:29

this gives us three acts times quantity x plus y

01:33

minus for why Tens quantity x plus y we've got

01:37

three x squared plus three x y bonnie's for x

01:39

y minus four y squared and yeah that gets us

01:42

three expert minus x y monies for y squared b

01:46

there that one's close but it's not quite right Switching

01:49

the signs makes the middle term positive See the positive

01:52

one there and switching the placement of the four and

01:55

the one makes the middle term too large We can't

01:58

do that So strategy change Send the factor pair two

02:01

times two in the battle instead So what we have

02:03

here Well Let's see we've got dead this x and

02:06

that's Why i'm thinking all right so we got three

02:07

explaining to why times x plus two why and that

02:11

pull out the three x there and that gets us

02:13

x plus two y minus two times exposed to why

02:16

and then the factors there Three x squared plus six

02:19

wide minus two Excellent on movements that kid says three

02:22

x squared plus for x y minus four y squared

02:25

Yeah there we go make like hercules and be proud

02:27

are great mathematical feats Leave us with the factors Three

02:30

x minus two why and Acts plus 2 like so

02:34

the answer is d

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