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]
