Question

factor z^3+125 im stuck on this

Answer 1

\[a^3 + b^3 = (a+b)(a^2 +b^2 - ab)\]

Answer 2

You can write 125 as \(5^3\)..

Answer 3

Using that formula now calculate

\[z^3 + 5^3 = ??\]

a = z and b = 5.

Answer 4

@jen89 , Go ahead..

What happened??

Answer 5

ummm im stuck well lost

Answer 6

Lost??

Where??

Answer 7

See, I have written the formula in my very first post..

There just replace a by z and by 5.. and then tell me what you got?

Answer 8

z^3+5^2(z+5)(z^2+5^2-z-5)

Answer 9

did i do that part right

Answer 10

\[z^3 + 5^3 = (z+5)(z^2 + 5^2 - z \cdot 5)\]

Answer 11

Now solve this further..

Answer 12

What is \(5^2\) ??

Answer 13

25

Answer 14

So finally you will get:

\[z^3 + 5^3 = \color{green}{(z+5)(z^2 + 5^2 - 5z)}\]

Answer 15

ok

Answer 16

@waterineyes, try teaching how to factor quadratic trinomials.

Answer 17

I did not get you @hero..

Answer 18

Example of quadratic trinomial:

\[15x^2 + 19x + 6\]

Answer 19

To whom I am teaching @hero?

You??

Answer 20

@jen89

Answer 21

See, here comparing with ax^2 + bx + c

a = 15, b = 19 and c = 6

To first find a*c = 15*6 = 90

Now I have to find the factors of 90 such that by adding them I will get 19 ie b..

Example: 2*45 = 90 but by adding 2 + 45, I will not get 19..
So first find two factors of 90 such that first factor + second Factor = 19..

Can you do this??

Answer 22

Okay, first tell me the possible factors of 90..

Example 15*6 = 90
2*45 = 90
3*30 = 90

Like wise..

Answer 23

ok 10 and 9 5 and 18

Answer 24

See that's what I mean

Answer 25

With the the other method, you have to guess more

Answer 26

You are telling this to whom?

Answer 27

To @jen89

Answer 28

Okay..

Have you come across quadratic polynomial earlier??

Answer 29

You both

Answer 30

We've done several together that I went over with her.

Answer 31

I teach the factor by grouping method as you already know.

Answer 32

mn = 90
m + n = 19

Answer 33

Using that method, it's is obvious the two numbers are 10 and 9

Answer 34

her??

Answer 35

Then from there, you can proceed to split the middle term

Answer 36

Is he her??

Answer 37

Yes....HER

Answer 38

Ha ha ha..
My mistake..

Answer 39

Anyway...

Answer 40

From there, you can split the middle term since 19x = 10x + 9x

15x^2 + 10x + 9x + 6

Answer 41

Then factor by grouping:

5x(3x + 2) + 3(3x + 2)
(3x + 2)(5x + 3)

Answer 42

If you use any other method, you'll have to guess more

Answer 43

ok thank you im trying realy hard to get this down pack

Answer 44

Now can I move from this post??

Answer 45

What do you mean "move from this post"?

Answer 46

I mean I have to go. I am in cafe using Openstudy.

I have to pay more charges if I don't move.. (

Answer 47

You don't need my permission to move bro.

Answer 48

Okay brother.. :)

A good enemies can be best friends.. It is a fact.. :)

Sorry if I have hurt you ever..

Answer 49

Trust me, you never hurt me.

Answer 50

im sorry for all of this

Answer 51

ok here another one z^3+27 so far i got (z+3) (z^2+3^2-3^2)

Answer 52

Almost but not quite. The problem is, if you're taking an online test, they will just say it is wrong.

Answer 53

Also, the way @waterineyes wrote the rule is not the way it should be written

Answer 54

\[(a^3 + b^3) = (a + b)(a^2 - ab + b^2)\]

Answer 55

27 is b right

Answer 56

No, 3 is b

Answer 57

and 3 cubed is 27

Answer 58

ok i see how u got the 3 now

Answer 59

ok i got (z^3+3^3) = (z+3) (a^2-z3+3^2)

Answer 60

You put a instead of z

Answer 61

And you should write -3z not -z3

Answer 62

Well, at least you were able to get this far.

Answer 63

(z^3+9)=(z+3)(z^2-3z+6)

Answer 64

Now you're just making it worse. You had everything right except for the a the first time. This time you just made it worse.

Answer 65

3^2 is not 6 and 3^3 is not 9

Answer 66

ok i see what i did hold on

Answer 67

ok 3^2 is 9 3^3 is 27

Answer 68

(z^3+27)=(z+3)(z^2-3z+9)

Answer 69

(z^3+27)=(z^3-3z+27) did i do that right

Answer 70

ok i think i messed that up is it (z^3+27) (z^3-3z^2+3z^2+27)

Answer 71

This is right:
(z^3+27)=(z + 3)(z^2 -3z + 9)

You second and third guessing yourself (not good)

Answer 72

Here's the thing. You need to learn how to multiply polynomials so that you can check your result

Answer 73

If I multiply (z + 3)(z^2 - 3z + 9) I should be able to get back to z^3 + 27

Answer 74

That's the only way to truly know if it is right

Answer 75

So let's do it and see:

(z + 3)(z^2 - 3z + 9)
= z^2(z + 3) - 3z (z + 3) + 9(z + 3)
= z^3 + 3z^2 - 3z^2 - 9z + 9z + 27
= z^3 + 27

Yep, I got back to z^3 + 27, so it must be correct.

Answer 76

When doing math, the key to being correct is being able to "check" your work. That's the key to mastering it. If you don't know how to check your work, you will never be good at math.

Answer 77

ok im trying to learn the steps you have been teaching me. i will keep working on this

Answer 78

Just don't confuse yourself in the process.

Answer 79

im trying not to

Answer 80

i feel bad for asking help all the time

Answer 81

Don't feel bad. Hundreds of students on this site have asked way more questions than you have. But you are actually trying to learn which I appreciate. It's okay to ask questions.

Answer 82

ok thanks :) by the way i tried one by my self and i want to show you the steps i did to see if i did it right

Answer 83

X^2+18x+81
mn=81 m+n=18 9 and 9
x(x+9x)+9 (9x+81)
(x+9) (x+9)

Answer 84

i think i checked my work right but im not shore i get the same as i started with

Answer 85

x^2+9x+9x+81
x^2+18x+81

Answer 86

You have the right end result, but your intermediary steps are flawed.