# Which Cubics are Irreducible?

**Algebra**Level 5

For how many positive integers \(1 \leq k \leq 1000\) is the polynomial \(f_k(x)=x^3+x+k\) irreducible?

**Details and assumptions**

A polynomial with integer coefficients is called **reducible** if it equals to a product of two non-constant polynomials with integer coefficients. Otherwise, it is called **irreducible**.