how do you factor this: -6x^4-12x^3+18x?

- anonymous

how do you factor this: -6x^4-12x^3+18x?

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- anonymous

ok, so what's something they all have in common?

- anonymous

6

- anonymous

great, and...

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- anonymous

and X?

- anonymous

yep, so you could all divide them by 6x.-6x^2 would be better, to get rid of the negatives. just an idea.
so you would then have:
-6x^2(x^2+2x-18)

- anonymous

i decided to divide it by -6^2, because we want our first value to be x^2, not x^3. we must also remember that the -6x^2 didn't just poof away. so we need to keep that. next we're going to factor for x^2+2x-18.

- anonymous

ok

- anonymous

do you think you can handle it from there, or do you want me to keep on going?

- anonymous

so when we factor x^2 + 2x - 18 the -6x^2 stays to the side?

- anonymous

do u mind helpin me with the next step?

- anonymous

so far i have (for factoring x^2 +2x-18) x(x )(x )....do u have to find 2 numbers that equal 18?

- anonymous

okay, im back sorry

- anonymous

yes and yes. you can just ignore the -6x^2 for now, and add it in the end. and you do need to find two numbers that equal -18, not just 18.

- anonymous

so first start of by list multiples of -18

- anonymous

ok cool... -6 x 3 = -18

- anonymous

so now i have x (x - 6) (x + 3)

- anonymous

ok, so now multiply it out and see if you get x^2 +2x-18

- anonymous

wait! i just noticed a huge mistake!

- anonymous

ok

- anonymous

we forgot to divide 18 by -6. so you need to factor for x^2+2x-3

- anonymous

i hope i didnt confuse you!

- anonymous

so now find factors for -3. this should be easier

- anonymous

we could use -1 and 3:
(x-1)(x+3)

- anonymous

sry my computer froze ...im lost now

- anonymous

so i shouldnt of used -18?

- anonymous

when we multiply that out, we get :
x^2+2x-3. which means this is right. remember how we divided -6x^2? well this is when we put it back. so the final factored answer is:
-6x^2(x^2+2x-3)

- anonymous

but where did the (x^2+2x-3) come from?

- anonymous

nevermind...I figured it out! lol ...i strolled back up in the convo

- anonymous

thank u so much...i just have 1 more quick question if u dnt mind

- anonymous

ok, remeber when we divided -6x^2? we forgot to divide that on -18x.

- anonymous

ok, lol. sorry for confusing you! i confused myself too. my cp kept freezing

- anonymous

my comp was freezing too!

- anonymous

Um...I think you factored -6x^2 out of 18x.

- anonymous

when factoring 27^3 - 48x ... being that there is no common numbers between the both of them...what would be the 1st step?

- anonymous

27^3 or 27x^3

- anonymous

im sry 27x^3

- anonymous

well then they can both be divided by x

- anonymous

ohh! wait a sec. what grade are you in?

- anonymous

so then i would have x(x )(x )...and then do i find #'s for 48?

- anonymous

im in 12th grade

- anonymous

have you learned about completing the square?

- anonymous

whoa! im teaching a 12 grader. sorry. im a freshie_

- anonymous

it doesn't sound familiar ... im really bad in math, its like another language to me!

- anonymous

lol well u did a good job helpin me on the 1st 1 =)

- anonymous

no prob, glad to help anytime

- anonymous

so the answer is :
-6x^2(x^2+2x-3)
for the first one

- anonymous

yea i got that 1

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