x^4-5x^2+4 don't have a clue how to factor?

I haven't had algebra in about 4 years and I don't have a clue on how to do this. The answer is (x+1)(x-1)(x+2)(x-2), but I haven't a clue on how they got this answer. If anyone knows how to factor this down, I would gladly appreciate it!!

fran2009-09-02T20:49:55Z

Favorite Answer

t =x^2 and (t >0) you have
t^2 -5t +4= 0
sovle you have t=4 ; t=1
<=> x^2 =4 --> x= + - 2
x^2 =1 --> x= + - 1

Faz2009-09-03T03:50:15Z

Treat this as a quadratic. To make it explicit let y=x² then
y² - 5y + 4
(y-1)(y-4)

Replace y with x² gives, and noting that they're difference of squares
= (x²-1)(x²-4)
=(x+1)(x-1)(x+2)(x-2)

oldteacher2009-09-03T03:55:47Z

it is a trinomial( 3 terms) this means you should try to find two binomials ( )( ) which multiply to give you this trinomial.

(x^2 -4)(x^2 -1) If you FOIL this, you will get the trinomial.

Notice that each () is the difference of two perfect square. The pattern is (x^2 -y^2)=(x-y)(x+y)

(x-2)(x+2)(x-1)(x+1)