Question

Math question!
Factor this expression:

X4 + 16 x2 + 256

Answer 1

Are you familiar with decomposition or "reverse FOIL" methods.

Answer 2

Decomposition, yes

Answer 3

What did you find ?

Answer 4

remember the one earlier with substitution
where you learn how to factor by grouping?
let u = x^2
the problem is now u2 + 16 u + 256

Answer 5

Ya that is right.

Answer 6

Thank you for reminding me :)

Answer 7

Apologies for the delay, its more complicated than simple decomposition, there's that extra step in this one, exactly what triciaal just explained.

Answer 8

Ok

Answer 9

The problem is what number multiplies to give 256 and adds up to give 16?

Answer 10

@lasttccasey what should I do, can you give me a hint?

Answer 11

You'll probably end up with imaginary numbers for solutions to this one. Give me a minute on that unless @triciaal knows a better way?

Answer 12

ok

Answer 13

@triciaal , do you know 2 numbers that multiply to give 256 and add to give 16?

Answer 14

I have the answer in my textbook. You can try to find the way. The answer is
16(x2-x+1)(x2+x+1)

Answer 15

@lasttccasey did you come up with anything?

Answer 16

Might be a stupid question but are we sure the equation we're trying to factor is:\[x^4+16x^2+256\]

Answer 17

I factored that a little bit, but in my textbook it asked to factor this:
16(x2+1)^2-4(2x)^2

Answer 18

My bad!

Answer 19

I thought I did it correct, I did a little bit and then I got stuck at it. I might have did It wrong.

Answer 20

This is the equation that we have to find:
16(x2+1)^2-4(2x)^2

Answer 21

lol yea I'm getting \[16x^4+16x^2+16\]

Answer 22

Ya it is confusing, but I guess I found an example similar to this question in my textbook. Anyway thanks for helping.

Answer 23

You're welcome, good luck!