We start with the polynomial expression: \[ -2 y^{2} - 24 y - 40 \]
The polynomial can be factored as follows: \[ -2 \left(y + 2\right) \left(y + 10\right) \]
The completely factored form of the polynomial is: \[ \boxed{-2 \left(y + 2\right) \left(y + 10\right)} \]
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