Saturday

December 20, 2014

December 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.

**Answer this Question**

**Related Questions**

Alegbra - Simplify the expression (3y+1)^2 + (2y-4)^2 I would start by expanding...

Algebra - I am solving sytems of equations algrbraically. I have tried several ...

Algebra - (4x^3-9x+8x^2-18)/(x+2)-use synthetic division to divide. I set it up ...

Algebra - I have to figure out how x^3+216=0 is factored, and what potential ...

Algebra Zero Product Rule - I'm working with the zero product rule and I've ...

Algebra - 8(a-b)2+14(a-b)-15 Is 8(a-b)2 supposed to mean 8(a-b)^2? If so, what ...

Pre-Algebra - Scatter plots are used to look for a pattern of association, or ...

Pre-Algebra - Complete the sentence below. Scatter plots are used to look for a ...

math - Factor 2x²+13x+40 I thought with this sort of problem you are supposed to...

Algebra - Could someone please help me find x in this problem and explain how ...