Question

Factor out the greatest common factor

Answer 1

@mathmate can you help me with this one too?

Answer 2

I think my common factor is 2x^2

Answer 3

what can each number take out?

Answer 4

@vshiroky that is right but ho would you write it

Answer 5

@vshiroky
Yes, take out the common factor that you identified, and then do the rest as a quadratic, if possible...

Answer 6

x2-6x3-6x

Answer 7

where did the 2x^2 go?

Answer 8

I don't know where to put it

Answer 9

Hang on give me 1 sec

Answer 10

ok

Answer 11

x^2 X 2x^2 - 3x X 2x^2 + 3x X 2x^2

Answer 12

Yes, after that you can write:
\(2x^4-6x^3+6x^2=2x^2(x^2-6x+6)\)

Answer 13

I have no clue what I just did btw

Answer 14

So what I just wrote was kinda on the right track?

Answer 15

\(x^2 X \color{red}{2x^2} - 3x X \color{red}{2x^2} + 3x X \color{red}{2x^2}\)

Answer 16

Ok so that part was right.. now what?

Answer 17

So this is my final answer 2x^2(x^2-6x+6)

Answer 18

You have to decide if (x^2-6x+6) has factors, what do you think?

Answer 19

no because nothing goes into x^2

Answer 20

Can you find two real numbers that have a product of -6 and a sum of 6?

Answer 21

Sorry backwards,
Can you find two real numbers that have a sum of -6 and a product of 6?

Answer 22

-3

Answer 23

and
@vshiroky

Answer 24

-3 and -3

Answer 25

so close

Answer 26

-3, -3 doesn't go, because -3*-3 gives 9, not 6.

Answer 27

ughhhhhh

Answer 28

Oh, didn't read the question well,
All you need is the GCF!
So you're done!

Answer 29

6

Answer 30

no, 2x^2, that you got at the beginning!

Answer 31

Oh I'm done already

Answer 32

omg

Answer 33

So my final answer is the 2x^2(x^2-6x+6)

Answer 34

Sorry, but the final answer is the GCF, which is \(2x^2\) . :)

Answer 35

That was wrong when I submitted it

Answer 36

Strike 2: the question says "factor out the GCF", and the answer says "write the answer in factored form", sorry my bad! (again)

Answer 37

It wants it submitted in factor form so wouldn't that be
2x^2(x^2-6x+3)

Answer 38

yes, indeed!

Answer 39

No that was wrong to and I have to start over

Answer 40

2x^2(x^2-3x+3) it should be

Answer 41

I have to do a whole different problem now

Answer 42

Sorry, I guess it's getting late for me here!
Do you have the new problem?

Answer 43

yes

Answer 44

Let's go for it!

Answer 45

Not bad, it's almost the same as the last one.
Tell me what your suggestion is.

Answer 46

I don't know the common factor because I would say 2^7 but that doesn't go into the other exponents

Answer 47

x^7 cannot be because you have terms in x^5.
The power of x in a common factor has to be the lowest so as not to have a negative exponent.

Answer 48

so 2x^5?

Answer 49

Excellent, that's the GCF, now try to get what's remaining.
Do not forget to divide ALL terms by the numeric factor!

Answer 50

I don't think I am doing this right

Answer 51

Tell me what you've got!

Answer 52

2x^2(x^5-2x^3-8x^3)

Answer 53

Reall: common factor is 2x^5, and there is a mistake in sign of the last term.
You're almost there!

Answer 54

2x^2(x^5-2x^3+8x^3

Answer 55

)

Answer 56

You would write it out as you did before:
common factor *....+ common factor *.... + common factor * ....

Answer 57

Why + the 2nd one?

Answer 58

is the second 2x^4 or 2x^3?

Answer 59

2x^4 for the factored second term is correct.

Answer 60

Ok so...
\[2x^2(x^5-2x^4+8x^3)\]

Answer 61

But it should be negative, since the original is negative.
Actually it's -2x
-4x^6 / (2x^5) = -(4/2) x^(6-5)=-2x

Answer 62

Remember: common factor is 2x^5 (not 2x^2).
The power is the lowest power of all three terms.

Answer 63

Then my whole thing is wrong

Answer 64

Just adjust the powers, the numbers are correct.

Answer 65

I mean the coefficients are correct.

Answer 66

I'm about to give up

Answer 67

You're almost there, hang in there.

Answer 68

\[2x^5(x^2-2x+8x^2)\]

Answer 69

You need to correct the power of the last term, because x^(5-5)=constant term.

Answer 70

This would be the last correction!

Answer 71

\[8x^5\]

Answer 72

That?

Answer 73

or just 8x

Answer 74

The way to check it is multiply 2x^5 by 8x will give you 16x^6 (which is not the original value).

Answer 75

The power is even lower than 8x.

Answer 76

I have no clue

Answer 77

You need a number when multiplied by 2x^5 that gives you 16x^5 (the original term).

Answer 78

just 8

Answer 79

Exactly.
SO what does the final answer look like?

Answer 80

\[2x^5(x^2-2x+8)\]

Answer 81

That looks good to me!

Answer 82

Let me know how it goes!

Answer 83

Its good
Thank you. I have to stop math now for the night before I cry some more lol

Answer 84

I need some sleep, badly! Sorry for the mistakes earlier. I hope the sleep will help!

Answer 85

Thank you for your help

Answer 86

You're welcome! :)