To complete the factoring of the polynomial \( -28z^9 \) as the product of two factors, we can start from the expression you provided:
\[ -28z^9 = -7z^6( __ ) \]
First, we need to identify the second factor by comparing \( -28z^9 \) with \( -7z^6 \) multiplied by some expression.
To find the second factor, we'll divide \( -28z^9 \) by \( -7z^6 \):
\[ \frac{-28z^9}{-7z^6} = 4z^{9-6} = 4z^3 \]
Therefore, we can conclude that:
\[ -28z^9 = -7z^6(4z^3) \]
So, the complete factored form is:
\[ -28z^9 = -7z^6(4z^3) \]
Thus, the blank can be filled in with:
\[ 4z^3 \]
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