The problem asks us to factor the polynomial $x^3 + 11x^2 + 30x$. If the polynomial can be factored, we need to write it in factored form. Otherwise, we say that the polynomial is prime.

1. Problem Description

The problem asks us to factor the polynomial $x^3 + 11x^2 + 30x$. If the polynomial can be factored, we need to write it in factored form. Otherwise, we say that the polynomial is prime.

2. Solution Steps

First, we can factor out an $x$ from each term:

$x^3 + 11x^2 + 30x = x(x^2 + 11x + 30)$.

Next, we need to factor the quadratic $x^2 + 11x + 30$. We are looking for two numbers that multiply to 30 and add up to

1

1. The numbers 5 and 6 satisfy these conditions since $5 \cdot 6 = 30$ and $5+6=11$. Thus,

$x^2 + 11x + 30 = (x+5)(x+6)$.

Therefore,

$x^3 + 11x^2 + 30x = x(x+5)(x+6)$.

3. Final Answer

$x(x+5)(x+6)$