- #1

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I don't understand how to factor a polynomial over Z

I need to factor the polynomail x

PLEASE HELP!!!

_{3}[x], Z_{7}[x], and Z_{11}[x]I need to factor the polynomail x

^{3}- 23x^{2}- 97x + 291PLEASE HELP!!!

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- #1

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I need to factor the polynomail x

PLEASE HELP!!!

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- #2

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mod 3:

X^3-23X^2-97X+291=X^3+X^2+2X=X(X^2+X+2). A calculation shows X^2+X+2 doesn't have a root in Z/3Z. Done.

mod 7:

X^3+5X^2+2X+4. A calculation shows it has no root in Z/7Z. The polynomial is irreducible.

mod 11:

291=5=1*5=10*6. So if the polynomial has a root, it should be 1, 5, 6, or 10. A calculation shows X^3-X^2+2X+5 has no root. The given poly is irreducible.

- #3

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I think I might have phrased this question wrong, but I figured it out.

THANKS

THANKS

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