1. **State the problem:** Factor completely the expression $$-46x^3 y z^4 - 29z$$. 2. **Identify the greatest common factor (GCF):** Look at each term: - First term: $$-46x^3 y z^4$$ - Second term: $$-29z$$ The coefficients are 46 and 29. The GCF of 46 and 29 is 1 because 29 is prime and does not divide 46. 3. **Look at the variables:** - The first term has $$x^3 y z^4$$. - The second term has $$z$$. The common variable factor is $$z$$ (lowest power of $$z$$ in both terms). 4. **Factor out the GCF:** Since the GCF is $$z$$, factor it out: $$-46x^3 y z^4 - 29z = z(-46x^3 y z^3 - 29)$$ 5. **Check if the expression inside parentheses can be factored further:** - $$-46x^3 y z^3 - 29$$ has no common factors and cannot be factored further. **Final answer:** $$\boxed{z(-46x^3 y z^3 - 29)}$$