Question

how do you factor x^4-10x^2+9=0

Answer 1

pretend X^4 as x^2

Answer 2

Essentially what louis said. Make a subsitution u=x^2

Answer 3

so its like y^2-10y^2+9=0

Answer 4

then when u get some thing like (y-21551515)(y-611919)
substitute x^2 back in

Answer 5

(BTW JUST made up the numbers.) i didnt solve it

Answer 6

i still dont undertsand..i can do the factoring for that equation but where does theother x^2 come in?

Answer 7

the factored form of that equation would be (y-9)(y-1) and then i do?

Answer 8

x squared and x squared, 2x and 5x, 1 and 2, and 3 and 3

Answer 9

x^4-10x^2+9=0

let u = x^2 and if we square u: u^2 = x^4

replace x^4 with u^2 and x^2 with u

u^2 - 10u +9 =0

solve for u

once you get u, solve for x: remember u= x^2 so x= ± sqrt(u)

Answer 10

I just factored this out, and not everything is able to be factorable @sanguinepenguin95

Answer 11

(y-9)(y-1) = 0

that means either (y-9) is zero or (y-1) is zero. you get 2 equations

y-9 =0
y-1=0

Answer 12

yo u guys are making it too hard for him....
loook once u get (y-9)(y-1)... put X^2 into the "y"s and solve

Answer 13

There are two monomials are not able to be factored @sanguinepenguin95

Answer 14

It is not able to be factored any more, because there are two monomials that can't be factored any further @sanguinepenguin95

Answer 15

so it would be (x+3)(x-3)(x+1)(x-1)?

Answer 16

then to check plug the answers back in the orignial equations and whatever doesnt equals ... u cross off that answers. they're called like extraneous values i believe

Answer 17

yes

Answer 18

Thankyou so much :)

Answer 19

x=3 -3 1 -1.... then plug them in the equation and whatever doesnt equals u cross them off

Answer 20

yeah no problem

Answer 21

I don't think I would do it quite that way.

after you find y= 9 and y=1
you use x = ± sq rt(y) to get
x= ± sqrt(9) and x= ± sqrt(1)
in other words:
x= +3, x= -3, x= +1 and x= -1

Answer 22

you have a 4th degree polynomial, so you should expect 4 (possibly repeated) roots.

Answer 23

... umm this is like alg 2 so id think theirs going to be 4th degree polynomial for this type of question..... maybe in calc or w/e

Answer 24

Actually, this problem is very typical of an algebra II course.