The problem asks to factor the polynomial $x^3 + 5x^2 + 4x + 20$.

1. Problem Description

The problem asks to factor the polynomial $x^3 + 5x^2 + 4x + 20$.

2. Solution Steps

We can try to factor the polynomial by grouping.

$x^3 + 5x^2 + 4x + 20 = (x^3 + 5x^2) + (4x + 20)$

Factor out $x^2$ from the first group and $4$ from the second group.

$x^2(x + 5) + 4(x + 5)$

Now, factor out the common factor $(x + 5)$.

$(x + 5)(x^2 + 4)$

$x^2 + 4$ cannot be factored further using real numbers, since the discriminant is $0^2 - 4(1)(4) = -16 < 0$.

3. Final Answer

$(x+5)(x^2+4)$