SOLUTION: hi....i really need ur help....i solved this problem but don't know if i get it correctly....thanks... factor: x^4 - 3x^2 + 1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: hi....i really need ur help....i solved this problem but don't know if i get it correctly....thanks... factor: x^4 - 3x^2 + 1      Log On


   

Question 106000: hi....i really need ur help....i solved this problem but don't know if i get it correctly....thanks...

factor:
x^4 - 3x^2 + 1
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4+-+3x%5E2+%2B+1
Let y=x%5E2
____y%5E2=x%5E4

Then,
y%5E2-3y%2B1
Read my lesson,"Factoring trinomials: SHORTCUT!!!" first then go back to this page.
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Using the quadratic formula,
y=%283%2B-sqrt%283%5E2-4%2A1%2A1%29%29%2F%282%2A1%29
y=%283%2B-sqrt%289-4%29%29%2F%282%29
Since sqrt%289-4%29=sqrt%285%29, which is irrational, this polynomial is not factorable.

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HyperBrain!