Question

w^2+4

Answer 1

If you want to solve for 0:
w^2 +4 = 0
w^2 = -4
w = +/- sqrt(-4)
w = 2i or w = -2i

Answer 2

what about factoring

Answer 3

w^2+4 is the same as w^2+0w+4


Can you find two whole numbers that multiply to 4 and add to 0?

Answer 4

2

Answer 5

2 and what?

Answer 6

-2

Answer 7

ok they add to 0, but they do NOT multiply to 4

Answer 8

right

Answer 9

so then there isn't another number?

Answer 10

Well you could try 2 and 2, but they don't add to 0

Answer 11

right

Answer 12

you can try 1 and 4, but again, they don't add to 0

Answer 13

etc etc

Answer 14

yes yes

Answer 15

You won't find any whole numbers that fit this description

Answer 16

So w^2+4 can't be factored

Answer 17

ohhhh

Answer 18

ok so what bout r^4-1

Answer 19

Write r^4 as (r^2)^2 and 1 as 1^2

So

r^4-1

is the same as

(r^2)^2 - 1^2

Answer 20

What's next?

Answer 21

\[w^2+4=(w+2i)(w-2i)\]

Answer 22

umm..(r^2-1)(r^2-1)

Answer 23

is that right?

Answer 24

you're close, it should be (r^2-1)(r^2+1)

Answer 25

Then factor r^2-1 further

Answer 26

(r-1)(r+1)?

Answer 27

yes

Answer 28

so r^4-1 completely factors to (r-1)(r+1)(r^2+1)

Answer 29

so the full answer is (r-1)(r+1)(r^2+1)

Answer 30

thank you I'm not very good at factoring

Answer 31

you got it, that's the final answer

Answer 32

ok i have another problem too that i can't factor

Answer 33

alright, go for it

Answer 34

8r^2-80r+128

Answer 35

What's the GCF here?

Answer 36

8

Answer 37

good, so factor this out to get ???

Answer 38

(8r-10)(r+16)

Answer 39

Not quite

Answer 40

Factor 8 from each term to get

8(r^2-10r+16)

Answer 41

(8r-16)(r-10)

Answer 42

Now factor r^2-10r+16

Answer 43

(r-8)(r+2)

Answer 44

close

Answer 45

(r-2)

Answer 46

better, so r^2-10r+16 factors to (r-8)(r-2)

Answer 47

which means

8r^2-80r+128

completely factors to

8(r-8)(r-2)

Answer 48

oh ok gotcha

Answer 49

\[\color{red}{w^2+4 \implies (w^2+4+4w)-4w.}\]\[\implies \color{blue}{(w+2)^2-4w.}\]\[\implies \color{blue}{(w+2)^2-(2\sqrt{w})^2.}\]Now it is in the form \[\color{green}{a^2-b^2=(a+b)(a-b).}\]

Answer 50

@Kristen123 gt it or nt?

Answer 51

Am I wrong anywhere?