Question

How do you factor this polynomial?

Answer 1

what polynomial?

Answer 2

(t)(h)(i)(s)

Answer 3

Very carefully.

Answer 4

\[3x ^{9}-768x\]

Answer 5

Find the GCF between the two terms.

Answer 6

factor out 3x and post what you get.

Answer 7

difference of cubes

Answer 8

I got 3(X^8-256) But Its marked wrong :/

Answer 9

You need to factor out a 3x

Answer 10

I did. Didnt I?

Answer 11

You put 3

Answer 12

And do you notice anything about x^8 - 256

Answer 13

\[3x(x^8 - 256)\]

Answer 14

no, math cruncher is wrong this is a difference of squares

Answer 15

\[x^8 - 256 = (x^4)^2 - (16)^2\]

Answer 16

What so the 3x disappears??

Answer 17

No, I'm just showing you that's what that equals.

Answer 18

3x(x^4 - 16)(x^4 + 16)

Notice anything about those?

Answer 19

No because you would multiply 3x with x^8. And that gives you 3x^9. Then multiply 3x with 256 and that gives you 768. So why is mine wrong? :/

Answer 20

Because it can be factored further.

Answer 21

You're not done yet.

Answer 22

Oooh I see. I still have to factor it more. OK.

Answer 23

But the final answer ends up being 3x(x^4 - 16)(x^4 + 16)

Answer 24

You will see a bunch of difference of squares. Just keep factoring them until you can't anymore.

Answer 25

Yeah, there's another difference of squares in that.

Answer 26

What?! the 16 can be factored again right?

Answer 27

3x(x^2 - 4)(x^2 + 4)(x^4 + 16)

Answer 28

And there's ANOTHER difference of squares in that :)

Answer 29

My its 2 right?

Answer 30

3x(x - 2)(x + 2)(x^2 + 4)(x^4 + 16)

Answer 31

Wow. Now that was a lot of factoring! But thats all we can factor it right?

Answer 32

I believe so.

Answer 33

Thanks so much! :)