Reducibility & Irreducibility, Eisenstein Criterion, Mod p test, reducibility test for degree 2 &3

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[simonrai]

Thank you very much Ma'am.
Highly recommended!

[SHREECHAMUNDAFILMUDD]

I am very confused please I need the answer
Why 2x^2+4 be reducible over z, ....Which has degree two or three, it must have at least one zeros belong to Z - according to the I know the concept of unit....But according to the theorem, the degree of its parts should be less than f[x]

[SHREECHAMUNDAFILMUDD]

A polynomial f (x) ∈ F[x] is reducible over F if we can factor it as f (x) = g(x)h(x) for some g(x), h(x) ∈ F[x] of strictly lower degree. If f (x) is not reducible, we say it is irreducible over F.
A polynomial f (x) ∈ F[x] is reducible over F if we can factor it as f (x) = g(x)h(x) for some g(x), h(x) ∈ F[x] of strictly lower degree. If f (x) is not reducible, we say it is irreducible over F.

[ayushkaprasad]

If a polynomila is irreducible over Z then we say its irreducible over Q ...counter example: 2x²+ 4 ....its is irreducible over Q but reducible over Z ...the statement at 19:52 is wrong

[MukeshKumarDansena-vkyc]

I think we can take p=3 instead of 11... It will also work

[SHREECHAMUNDAFILMUDD]

Why 2x^2+4 be reducible over z, ....Which has degree two or three, it must have at least one zeros belong to Z - according to the I know the concept of unit....But according to the theorem, the degree of its parts should be less than f[x]A polynomial f (x) ∈ F[x] is reducible over F if we can factor it as f (x) = g(x)h(x) for some g(x), h(x) ∈ F[x] of strictly lower degree. If f (x) is not reducible, we say it is irreducible over F.

[sachin.kumar-meher]

Mem p^2= 25, 25 kaise 5 ko decide nahi Karega