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Show that over the ring Z/30Z[x] the polynomial f(x)=x has the factorization f(x)=(10x+21)(15x+16)(6x+25)

Let f(x)=x* +x² +2 be a Polynomial in Z3[X]. Which of the following statements is True O f(x) is reducible over Z, None O f(x) is irreducible over Z,

Use Eisenstein's criterion to show that the polynomial x3 –- 3x? + 9x – 10 is irreducible over the field of rationals Q.

Suppose f(2) = anz is entire. If f(z)| ≤ 3|2|ln(|z] + 1) for all z, prove that f is a polynomial.

If f(x) and g(2) are monic polynomials of minimal degree for which A is a root then f(1) = g(1). True False

f(x)=x²-3 is the minimal polynomial of √3 over Q,