1. **State the problem:** We need to factor the polynomial $$w^6 - 7w^3 + 10$$. 2. **Rewrite the polynomial:** Notice that $$w^6 = (w^3)^2$$, so let $$x = w^3$$. The polynomial becomes $$x^2 - 7x + 10$$. 3. **Factor the quadratic:** We look for two numbers that multiply to 10 and add to -7. These numbers are -2 and -5. 4. **Write the factored form:** $$x^2 - 7x + 10 = (x - 2)(x - 5)$$. 5. **Substitute back:** Replace $$x$$ with $$w^3$$ to get $$ (w^3 - 2)(w^3 - 5)$$. 6. **Check the options:** The correct factorization matches option D: $$(w^3 - 2)(w^3 - 5)$$. **Final answer:** $$(w^3 - 2)(w^3 - 5)$$