The problem is to factor the polynomial $x^4 - 5x^2 - 50$.

1. Problem Description

The problem is to factor the polynomial $x^4 - 5x^2 - 50$.

2. Solution Steps

Let $y = x^2$. Then the polynomial can be written as $y^2 - 5y - 50$. We need to find two numbers that multiply to $-50$ and add up to $-5$. Those numbers are $-10$ and $5$. Thus we can factor the polynomial in terms of $y$ as $(y - 10)(y + 5)$.

Now we substitute $x^2$ back in for $y$ to get $(x^2 - 10)(x^2 + 5)$.

$x^2 - 10$ can be written as $(x - \sqrt{10})(x + \sqrt{10})$, but the problem most likely wants integer/rational solutions.

$x^2 + 5$ can be written as $(x - i\sqrt{5})(x + i\sqrt{5})$, but again, the problem likely wants real solutions.

So we have $(x^2 - 10)(x^2 + 5)$.

3. Final Answer

$(x^2-10)(x^2+5)$