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October 20, 2014

October 20, 2014

Posted by **Katie** on Thursday, October 8, 2009 at 6:33pm.

- Algebra -
**MathMate**, Thursday, October 8, 2009 at 6:39pmIf you factorize the polynomial in two steps, you will see it more clearly.

X^4-3x^2+2

easily factorizes into two factors:

(x²-2)(x²-1)

Each of the above factors factorizes into two others by virtue of the identity

(a²-b²)=(a+b)(a-b)

The factor (x²-2) does not have a*rational*factor, but it can still be factored as

(x²-2)=(x+√2)(x-√2)

and the second one, as you have already done:

(x²-1)=(x+1)(x-1)

So the polynomial actually has four factors, two of which are irrational, and four corresponds to the degree of the polynomial.

Since

(x+√2)(x-√2)(x+1)(x-1)=0,

it should be quite clear why the four zeroes are where they are.

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