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Applying Eisenstein's criterion to verify if a polynomial is irreducible or not. For example: x^3+4x^2+3 We choose p=3. We can't apply Eisenstein's criterion on this polynomial because the non-leading coefficient 4 is not divisble by p. But if we have for example: x^3+6x^2+3 we could apply the criterion because the non-leading coefficients 3 and 6 are divisible by p. Is this correct?

Applying Eisenstein's criterion to verify if a polynomial is irreducible or not. For example: x^3+4x^2+3 We choose p=3. We can't apply Eisenstein's criterion on this polynomial because the non-leading coefficient 4 is not divisble by p. But if we have for example: x^3+6x^2+3 we could apply the criterion because the non-leading coefficients 3 and 6 are divisible by p. Is this correct?

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 46E
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Applying Eisenstein's criterion to verify if a polynomial is irreducible or not.

For example: x^3+4x^2+3

We choose p=3.
We can't apply Eisenstein's criterion on this polynomial because the non-leading coefficient 4 is not divisble by p.

But if we have for example: x^3+6x^2+3 we could apply the criterion because the non-leading coefficients 3 and 6 are divisible by p.

Is this correct?

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Yes it is correct

 

For example: x^3+4x^2+3

 

We choose p=3.

We can't apply Eisenstein's criterion on this polynomial because the non-leading coefficient 4 is not divisble by p.

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