1. **State the problem:** Factor the expression $$8u^9v^6 - 24u^3v^2x^4$$ by factoring out the greatest common monomial factor. 2. **Identify the greatest common factor (GCF):** - For the coefficients: GCF of 8 and 24 is 8. - For the variable $u$: minimum exponent is $3$ (since $u^9$ and $u^3$), so factor out $u^3$. - For the variable $v$: minimum exponent is $2$ (since $v^6$ and $v^2$), so factor out $v^2$. - Variable $x$ appears only in the second term, so it is not part of the GCF. 3. **Write the GCF:** $$8u^3v^2$$ 4. **Divide each term by the GCF:** $$\frac{8u^9v^6}{8u^3v^2} = u^{9-3}v^{6-2} = u^6v^4$$ $$\frac{24u^3v^2x^4}{8u^3v^2} = \cancel{\frac{24}{8}}1 \cancel{\frac{u^3}{u^3}}1 \cancel{\frac{v^2}{v^2}}1 x^4 = 3x^4$$ 5. **Write the factored form:** $$8u^3v^2(u^6v^4 - 3x^4)$$ 6. **Final answer:** $$\boxed{8u^3v^2(u^6v^4 - 3x^4)}$$