Question

Factoring cubes/Solve by factoring: How do I do this when it is a problem that is to the 4th power?

X^4-625

Answer 1

What number times 4 will give -625? You could go through polynomial division but its not worth it because its a perfect quartic.

Answer 2

5

Answer 3

Exactly, so how does that look once you reduce both parts by the fourth power?

Answer 4

x-5

Answer 5

Ill be honest with you and say that I can't 100% continue on from here. Could someone else take over?

Answer 6

rosey, we'll have to do something similar that we did in #2 of the last problem set. Remember how we messed with the power?

We don't have a way of reducing 4th powers, but do you remember a formula for the difference of SQUARES? :)

Answer 7

It's ok. Thanks for trying

Answer 8

No I do not refresh my memory please

Answer 9

"What number times 4 will give -625"

?? -625 / 4 = 156.25

Try this: What number raised to the fourth power is 625? 5^4 = 625

Somehow, you understood that and got it right. Kind of amazing.

Answer 10

\[\large a^2-b^2=(a-b)(a+b)\]
We want to utilize this formula :)

Answer 11

Ok.

Answer 12

\[\huge x^4=x^{2*2}\]
Remember how we rewrote that as a lower power last time? :D

Answer 13

YES

Answer 14

I was trying to do that on my own but it wouldn't add up to the 4th power when putting into the cube formula. I guess I was using the wrong formula?

Answer 15

you could apply the cube formula, but you would have fractional exponents, it would look really really ugly! :)
Because you would rewrite:\[\large x^4=x^{(4/3)3}=(x^{4/3})^3\]

Answer 16

oh no - I don't want that. It looks ugly

Answer 17

We have really nice formulas for the difference of SQUARES, and difference of CUBES. When you look at your problem, try to identify if the power is a multiple of 2 or 3, that might help you figure out which rule to use.

Answer 18

multiple of 2

Answer 19

I got it

Answer 20

\[\large x^4-625=x^4-5^4=x^{2*2}-5^{2*2}=(x^2)^2-(5^2)^2\]
Ok understand what's going on now? :D yay

Answer 21

\[(x ^{2}+25)(x+5)(x-5)\]

Answer 22

Ok good good :) So you recognized the difference of squares in your answer, so you broke it down another time. yay rosey! \c:/

Answer 23

YEAYYYY. Cool thank you so much!!!!