Question

factor z^3 - 3z^2 + 3z - 1

Answer 1

either z(z2-3z+3)-1 or z3-3z(z-1)-1

Answer 2

z^2(z - 3)+3z-1..... something is weird about this

Answer 3

i got the same answer as you hero...... i know it is

Answer 4

Are you sure you wrote it down correctly?

Answer 5

Its a work packet :/

Answer 6

Wait...let me see something real quick...hold on...

Answer 7

k

Answer 8

The next problem is the same way, x^3 + 15x^2 +75x + 125

Answer 9

yes this is about factor and remainder theorem
am gonna show my competence
watch out for me now

Answer 10

I think you have to re-write it like this:

\[-3z^2 + 3z + z^3 -1\]

Answer 11

Then factor as follows:

Answer 12

hero you're amazing

Answer 13

makes sense now <3

Answer 14

the last two terms are difference of cubes

Answer 15

you're a boss thanks

Answer 16

Ooooh wait....lol

Answer 17

yeah i know i caught your mistake im good now haha

Answer 18

\[-3z(z-1)+(z-1)(z^2+z+1) = (z-1)(z^2-2z+1)\]

Answer 19

There ya go

Answer 20

Is that what you get too?

Answer 21

i got the first half of what you last wrote as my answer

Answer 22

Yes, but it isn't done unless you use distributive property. z - 1 is common to both

Answer 23

The final answer I got is the correct answer.

Answer 24

It may even be able to be simplified further...

Answer 25

yep, it can...\[(z-1)(z-1)(z-1)\]

Final Answer!

Answer 26

BIZARRE!

Answer 27

the question is really correct

Answer 28

i think you made a mistake hero i dont see how you could distribute beyond my answer

Answer 29

Yes, the question is really correct, and the complete factorization is a product of three binnomals

Answer 30

I didn't make a mistake. You just don't understand that you need to use distributive property when factoring if you have two common binomials. Your answer is not a complete factorization

Answer 31

I can prove that my factorization is correct

Answer 32

And actually, it can even be simplified further to: \[(z-1)^3\]

Answer 33

scroll down to the "expanded form":

http://www.wolframalpha.com/input/?i=%28z-1%29%28z-1%29%28z-1%29

Answer 34

hero is right but i got a new method
see it now..

Answer 35

A-grade....Post It!

Answer 36

the question needs not t be written again..
;et
z^3-3z^2+3z-1

Answer 37

Are you sure 'bout that?

Answer 38

And what happened to the OP?

Answer 39

−3z(z−1)+(z−1)(z^2+z+1)=(z−1)(z^2−2z+1) i still dont get how you did that

Answer 40

\[ab + ac = a(b+c) \].....think about it: \[a = z-1; b = -3z; c = z^2+z+1 \]

Ponder it for a while............. and don't forget to check wolfram alpha...

Answer 41

first of all let
f(z)=z^3-3z^2+3z-1
let us now find a number to replace z which would make the function 0, zero
that number is 1
so,
f(1)=1^3-3*1^2+3*1-1
this gives us 0, zero
now,
z=1
z-1=0
hence (z-1) is a factor
now divide the original question by (z-1)
and you would get z^2-2z+1
factorise this too by quadratic theorem and you would get
(z-1)(z-1)


and so the final answer is (z-1)(z-1)(z-1)

please this is under factor and remainder theorem.....

Answer 42

thats why it didnt make any sense you said you distributed but you just factored out the (z-1)

Answer 43

I said I used "distributive property"

Answer 44

But yeah, I factored out the z -1

Answer 45

Well, at least you understand now...

Answer 46

yup

Answer 47

Grade A....If your method works so great, how come I still did a complete factorization and posted the answer before you did?

Answer 48

It's not a comparing wingspan sizes contest, different people arrive at the answer in different ways.

Answer 49

My argument is, he came up with his "answer" after I'd already posted the answer. In other words, he already knew what the factors were AFTER THE FACT....I gave him a medal, but still...

Answer 50

Anyways, we can work on that next one...

Answer 51

Unless you already have it.

Answer 52

yeah it took me like 15 seconds

Answer 53

Oh nice...What did you get?

Answer 54

(x+5)^3

Answer 55

Perfect!

Answer 56

You're getting the hang of this. Your teacher will be proud

Answer 57

hero dnt be annoyed at all'
mathematics is never one way
mathematicians use several means to arrive at the same answers

Answer 58

Either way, you still posted your solution after the fact. Any reason why it took you so long?

Answer 59

Almost 20 minutes after I posted my solution

Answer 60

I'm not even including when I first started working on this. That's 20 minutes after I posted my solution only. So, if it really takes that long to do it your way, I'm good..