Question

Divide. 18x^3+12x-3x/6x^2
@mjoxprm360

Answer 1

do u know how to do this @mjoxprm360

Answer 2

Do you know how to factor 18x^3 + 12x – 3x?

Answer 3

well no is it lik but lik terms toghther or something

Answer 4

So, what's the greatest common factor of 18x^3 + 12x – 3x?

Answer 5

i think 3 am i right

Answer 6

haha wait wait wait here

Answer 7

ok wat u fina do??

Answer 8

do you know how to find the GCF? If not, I can walk you through it.

Answer 9

need a walk through?

Answer 10

well yes i do

Answer 11

Okay, so first we need to list all the prime factors of the coefficients. The coefficients are 18, 12, and 3.
3: 3
12: 2, 2, 3
18: 2, 3, 3

Now, I want you to tell me what one prime factor all of the coefficients have in common.

Answer 12

i know how to find the GCF

Answer 13

ok they all have 3 in common i just wanted to explain why

Answer 14

do you know how to factor the GCF out?

Answer 15

?

Answer 16

yes

Answer 17

ok good can you tell me what your answer for the gcf is?

Answer 18

yes i do know how to

Answer 19

3

Answer 20

We need to put the GCF on the left side of a set of parenthesis. Like this:
3x( )
And now we need to figure out what to put in those parenthesis. And in order to do that, we need to figure out what we can multiply by 3x to get our original expression, 18x^3 + 12x – 3x. 3x times what equals 18x^3?

Answer 21

ok

Answer 22

so i multiply

Answer 23

Dang, okay, don't be mad at me, but I think I read your question wrong. At first, we were supposed to combine the like-terms 12x and –3x which would equal 9x. 18x^3+9x.
Are you okay with starting from scratch? It won't take as long this time since you understand the concepts.

Answer 24

i would never get mad at u

Answer 25

ok im okay with that

Answer 26

Yay, okay! :D
We have 18x^3 + 9x. We need to find the GCF of this expression, just like last time. Do you know how to do that now?

Answer 27

yes

Answer 28

the GCF is 3

Answer 29

Yes, that's a factor of both of them, but not the GREATEST common factor. :D So let's list the prime factors of the coefficients, 18 and 9.
9: 3, 3
18: 2, 3, 3
They both have two 3's in common, right? We would multiply the two 3's to get the number 9. That's the first part of our GCF. Since our terms both have at least one x, we can also add the x to our GCF. So, the GCF is 9x. Does it make sense how we got that?

Answer 30

yess it does

Answer 31

Okay, we need to put it on the left side of a set of parenthesis just like last time:
9x( )
Remember our original expression, 18x^3 + 9x.
9x times what equals 18x^3?

Answer 32

idk :( um. is it 3x+2

Answer 33

2x^2

Answer 34

ohh ok

Answer 35

so wats the answer

Answer 36

9x(2x^2+1) Now we factored out our first term (18x^3), and now for our second term (9x).
In order to get 9x from 9x, we just multiply by 1, correct? So, this is our factored form of the expression:
9x(2x2∗1)

That's just the numerator, though. We need to find
9x(2x2+1)6x2


The denominator (6x^2) doesn't need to be factored. Now that we have both the numerator and the denominator factored, we can begin to divide out terms. Do you know how to do that?

Answer 37

You divide like terms

Answer 38

um........ noo but is it jus dividing the like terms

Answer 39

9x(2x2+1)6x2


Do you know what the greatest common factor of 6 and 9 is? In other words, what's the greatest number than can divide into both of them?

Answer 40

its 3 again

Answer 41

Yes! So 9÷3 is 3, and 6÷3 is 2. We can divide those out so we get:
3x(2x2+1)2x2

Do you see that both the numerator and the denominator have at least 1 "x" in them? (The numerator has 1 x, and the denominator has 2 x's.)

Answer 42

That is, at least one x outside of the parenthesis

Answer 43

ok yea i see that

Answer 44

Okay, good. So we can cancel out 1 "x" from the numerator and the denominator.
3(2x2+1)2x


Since we can't divide anything else out, that would be your answer. Does it make sense how we got that?

Answer 45

yes it does

Answer 46

great!

Answer 47

XD awesomee

Answer 48

so wats the answer

Answer 49

\[3(2x ^2+1 \frac{ 2 }{ x }\]

Answer 50

thanx ndf u sure

Answer 51

wait is that the answer

Answer 52

3(2x2+1)2x

Answer 53

ok thanx