'Rooty' polynomials!(part 2)

Algebra Level 4

Let \(f(x) = x^3 + 2x^2 + 3x + 2\) and \(g(x)\) be a polynomial with integer coefficients. When \(f(x)\) is divided by \(g(x)\), it leaves quotient \(q(x)\) and remainder \(r(x)\), both of which have integer coefficients.

If \(q(x) = r(x) \neq 1\) ,then find \(g(5)\).

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