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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!!
3 Answers
- 1 decade agoFavorite 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
- FazLv 71 decade ago
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)
- oldteacherLv 51 decade ago
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)
