ShmoopTube

00:03

Okay Shmoop math people got more drills What is the

00:06

fully factored form of the polynomial Negative sixty next to

00:09

the six plus eighty one x squared Yeah Okay Is

00:16

it just us or are polynomial unnecessarily scary looking to

00:20

the unprepared They could be downright terrifying but this isn't

00:23

too bad of a problem if we take it step

00:24

by step So we start by factoring out negative one

00:26

to make the leading term positive and just looks like

00:29

that And sixteen and eighty one don't have any common

00:32

factors But we can factor out x squared from the

00:35

next in the sixth and the square there Right So

00:38

now notice that both sixteen x the fourth and anyone

00:41

are perfect squares Yes your hunch was right since four

00:44

x squared then squared is sixty next the fourth and

00:47

nine squares Eighty one Well they follow the pattern of

00:50

a difference of squares problem And when we see terms

00:52

that fit into the pattern a squared minus b squared

00:54

well we can factor to a plus b and an

00:57

a minus b that looks like that That means we

00:59

didn't factor that last term Sixteen x the fourth minus

01:02

eighty one And it'll look like that negative x squared

01:05

for tripolis nine for its foreign minus nine And finally

01:08

we noticed that now we have another difference Of squares

01:10

in the last binomial term Therefore x squared minus nine

01:13

Since you know to x squared is for x squared

01:16

and three export is nine Right So we have ah

01:20

for x squared there and well yeah three squared is

01:24

nine All right Time to factor yet again Well what

01:27

does that give us That gives us negative x squared

01:29

over here Times quantity for x where plus nine times

01:31

quantity to explode three times quantity to x minus three

01:34

While poly means many and no meal means well my

01:39

mother said no dinner until we finish studying Right Well

01:42

we're one step closer to father bears a scarier than

01:45

a polynomial meatloaf with this answer So whatever That's the 00:01:49.12 --> [endTime] answer Yo Whoa

Full Transcript