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Find the binomial that completes the factorization.

[tex]\[ 125q^3 - 1 = \left(25q^2 + 5q + 1\right) \cdot (\text{binomial}) \][/tex]

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GinnyAnsweridn
To find the binomial that completes the factorization of the polynomial [tex]\(125q^3 - 1\)[/tex], we should factorize the given polynomial completely.

We start with the polynomial:
[tex]\[125q^3 - 1\][/tex]

It can be factored as:
[tex]\[125q^3 - 1 = (5q - 1)(25q^2 + 5q + 1)\][/tex]

Here, [tex]\((5q - 1)\)[/tex] is the binomial that completes the factorization. Therefore, the complete factorization of the given polynomial is:
[tex]\[125q^3 - 1 = (5q - 1)(25q^2 + 5q + 1)\][/tex]
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