Quotient of ring of polynomials over ℤ

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The quotient ℤ[X]/(X-3) is isomorphic to ℤ. But here f(x) = x-3 is reducible in ℤ[X] because it has root 3 in Z. So how come the quotient is isomorphic to ℤ (in which case it will be an integral domain).