Question

9x^2(2x+7)-12x(2x+7)=3x(2x+7)(3x-4) ...at the end where did the (3x-4) come from?

Answer 1

As far as I can tell; you typed it in there. :)

Answer 2

It's on the website where I found this openstudy group. I never answered it. It says that's the answer and I'm a bit confused.

Answer 3

You have 2 numbers that are the same (2x+7) and (2x+7); so factor those out and your left with:

(2x+7) (9x^2-12x) does this make sense?

Now, we can factor (9x^2 -12x) even further to get:

3x (x-4) ; it should be:

(3x) (2x+7) (x-4). It would be a typo :)

Answer 4

ack!! my mistake

3x(3x-4) is correct... do you know why?

Answer 5

No, I don't know why. xD I have a math 11 test tomorrow and I'm a bit nervous. I can't get the hang of this stuff. :/ Mind explaining?

Answer 6

do you understand the first step....how to factor out (2x+7) and get left with (9x^2 -12x)? It is the opposite of distirbuting...

Answer 7

The question is 9x^2(2x+7)-12x(2x+7) and I know that theres a 3x in each term and a (2x+7) so you can factor those out right? So on the site it says it equals 3x(2x+7)(3x-4) and I understand how I got the 3x(2x+7) because both terms have it, but I'm so lost as to where the 3x-4 came up.

Answer 8

lets take it step by step and you will see where it comes from...fair enough?

Answer 9

Kay. :)

Answer 10

9x^2(2x+7)-12x(2x+7) has a common factor that is blaringly obvious. It is (2x+7) right? just let me know if this is correct....

Answer 11

Yes, but doesn't it have 3x as well?

Answer 12

3x doesnt matter yet; it will come, but not yet. lets clean it up some first ok?

Answer 13

kk, so yes, 2x+7

Answer 14

when we factor out (2x+7) are we left with:

(2x+7) (9x^2 -12x) ? yes or no...

Answer 15

think of (2x+7) call it A if you have to..

Answer 16

yes, we're left with it.

Answer 17

sorry i'm talkign long to reply. keep pressing enter instead of post.

Answer 18

taking.*

Answer 19

its ok...

Now we can factor (9x^2 -12x). Do you see how we could do that?

Answer 20

Oh wait! So, you can take out a 3 because of 9 and 12, and you can also take out an x, hence 3x, and you can get a 4 because 3X4 = 12.

Answer 21

you are brilliant :)

Answer 22

So 3x(3-4)

Answer 23

So once we get that we just put the 2x+7 back in?

Answer 24

And our 3x would go in front.

Answer 25

3x(3x - 4) = 9x^2 -12x right?

Answer 26

but yes, you can put the numbers back in whatever order you feel comfortable with.

Answer 27

yes! :D

Answer 28

So that's why there was a 4. I was confused about that but now I get it, because of the 3-4, 3x4= 12. Makes so much more sense now.

Answer 29

Just remember to take things step-by-step and it should all work out :)

Answer 30

I'm still bad at this stuff, though. I understand that question, but there's like 4 different types of facorting we're doing in class and I get confused when I'm doing problems because I'm not sure which one I'm supposed to use.

Answer 31

I hate the way they teach factoring in school. Because there is only one method that you actually use.. it is to "un" distribute or take apart; what was already put together.

Answer 32

& my math teacher picks favorites, if you're not up there in your math grades then he'll get mad. It's really annoying. I failed my past two math tests. I had 88 on my first test, but when he started teaching I dropped down to half that mark, to like 44. Tomorrow's test is kinda crucial.

Answer 33

what factoring methods do you need help with?

Answer 34

I'm strong in every other subject besides math. Anyways, care to help me with a couple more problems?

Answer 35

I'll list a problem I was having trouble with today. One second, I'll find it in my book.

Answer 36

x^2+8x+12
x^2+3x-18

and it's supposed to be over each other.

Answer 37

The top part = (x+2)(x+3) right?

Answer 38

glorified fractions is all that is.

The equation gives you clues as to what to do. Do you see the "sign" of the last term?

Answer 39

What sign? I'm not sure what you mean by that, sorry.

Answer 40

(+12) OR (-18)

the last term is gotten by multipying 2 numbers together.

What combination of "signs" when multiplied give you a (+) answer?

What combination of "signs" when multiplied give you a (-) answer?

Can you tell me?

Answer 41

two positives = positive, two negatives = positive, and a - and a + = a -, right?

Answer 42

thats right. So the last term gives us a clue about our middle term. Becuase the middle term takes those same 2 numbers and adds them together.

Lets focus on the top: +8 +12.

we need 2 numbers that are either (-)(-) or (+)(+) to get the (+12) right?

and they need to add together to get a (+) for the middle term (+8).

Does this make sense?

Answer 43

Yeah that makes sense, we're trying to get a LCD?

Answer 44

2 and 6?

Answer 45

we will soon enough; but lets take it step by step.

We can start to set up our answer like this: Good now...

(x 2 ) (x 6 ) what "sign" do we need to use to fill this in? to get a (+12) and a (+8)

Answer 46

+

Answer 47

Yes, (x+2) (x+8) is the answer for the top; store it away somewhere where it wont get broken...

Answer 48

opps... make that (x+2)(x+6) and feel free to correct me :)

Answer 49

That's the answer for the top? Don't the 6 break down to a 3? Or we can't do that because we're only going half of 12?

Answer 50

there is nothing that x and 6 have in common so it is as far as it will go. to double check, multiply them back together.

Answer 51

I understand.

Answer 52

x^2 +3x -18 the last term tells us what signs we need to use. and the middle term tells us which of those signs gets the bigger number. Does that make sense?

Answer 53

what makes a (-) when multiplied together?

Answer 54

+ and -

Answer 55

I don't know what you mean by which sign gets the bigger number, though.

Answer 56

good; then its our only option:

(x+ )(x- ) is what we are dealt. now find 2 numbers that multiply to 18 and "subtract" to get 3.

Do you see why we need the (+)number to be bigger than the (-)number to get (+3)?

Answer 57

I'm a bit confused.

Answer 58

the numbers are gonna be 6 and 3... to equal 18 right?

-6 +3 = -3

+6 -3 = +3

do you see it?

Answer 59

I thought we were trying to equal 18? Not - and +3?

Answer 60

-3*

Answer 61

ok...we can do that as well; what are the factors of 18 that subtract to get (+3) for a middle term?

1 and 18
2 and 9
3 and 6

thats it... right?

Answer 62

yep

Answer 63

one number has to be (-) and the other number has to (+)

In order to get the (+3) for the middle term, the largest number has to be (+)

such as: +6 -3 = +3

and +6 times -3 equals -18

does this make sense?

Answer 64

yes, it does!

Answer 65

then we can fill in our stuff now:

(x +6) (x -3) is our answer. for the bottom.

Can we cross anything out from top to bottom that are alike?

Answer 66

x+6

Answer 67

Good, and we are left with:

(x+2)(x+6) (x+2)
---------- = -----
(x+6)(x-3) (x-3)

Answer 68

so then it's gonna be x+2 over x+3

Answer 69

haha yep!

Answer 70

wait, -3

Answer 71

thats what I had written down on paper, typo on here. lol.

Answer 72

i wish I had time for more, but my macroeconomics class is starting and running for the next 2 hours.

You can do this, it is really stuff you already know :)

Answer 73

Thanks for your help, and perfect timing. I have to go right now too.