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PSAT 1.39 Math Diagnostic 184 Views


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Description:

PSAT 1.39 Math Diagnostic. Which of the following is equivalent to this expression?

Language:
English Language

Transcript

00:00

Sorry And here's your shmoop du jour brought to you

00:05

by birthday clowns Don't worry about it when you see

00:08

one of them crying in his van after the party

00:10

That's just how clowns express joy which of the following

00:14

is equivalent tio this times this and here the potential

00:18

answers ugly All right well this is the type of

00:21

problems we like to call a birthday clown It looks

00:25

terrifying at first but once you give it a chance

00:27

well it's not so bad This thing is seriously ugly

00:29

though and we can pretty it up with minimal effort

00:33

Really just a factoring exercise Each of these polynomial can

00:36

be broken down and factored And once we've done that

00:39

we'll be able to cancel out numbers like nobody's business

00:42

So yeah let's get started a sap so we don't

00:44

have to look at this thing anymore The polynomial in

00:47

the numerator on the left hand side x squared minus

00:49

for x minus twelve will factor into the quantity x

00:53

minus six and the quantity x plus two the other

00:55

numerator x squared plus two x minus fifteen factors into

01:00

the quantity x plus five and quantity x minus three

01:03

Well first denominator x squared plus seven x plus ten

01:07

factories into the quantity x plus five and quantity x

01:10

plus two and finally the other denominator x squared minus

01:14

eight Acts plus 12 factor's india the quantity x minus

01:17

six and the quantity x minus two remember the key

01:20

is to think of the possible factors of the last

01:22

term in the polynomial and then think about how you

01:25

could get to that middle term by either subtracting or

01:28

adding those factors together Well things get slightly trickier when

01:32

there's a coefficient other than one in front of the

01:34

first term But fortunately we don't have to worry about

01:36

that here So for example with the first polynomial we

01:39

know twelve is gonna factor into twelve and one and

01:43

six and two or four and three but only by

01:47

factoring into six and two can we get to the

01:49

four coefficient of the ex term And just like that

01:53

we're starting to see all this nastiness melt away Yeah

01:56

it's just like the end of frozen Now comes the

01:59

easy and fun part because we're multiplying these two fractions

02:03

together we can simplify from one uber long numerator and

02:07

one uber Long denominator and then cancel anything we see

02:11

on both top and bottom which is just about everything

02:13

right So the x minus six goes the x plus

02:16

two goes and the expos five is out of here

02:19

as well leaving just ex ministry over x minus two

02:23

which can't be simplified any further and conveniently enough That's

02:26

option a Okay so maybe you do your next birthday

02:29

at six flags Instead you're getting too old for clowns 00:02:31.97 --> [endTime] anyway Boy there he goes

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