1. **State the problem:** Factor the expression $$-2x(16x^2 - 40x - 25)$$ using the MT (Middle Term) Test Method. 2. **Recall the MT Test Method:** This method is used to factor quadratic expressions of the form $$ax^2 + bx + c$$ by finding two numbers that multiply to $$a \times c$$ and add to $$b$$. 3. **Identify coefficients:** Inside the parentheses, the quadratic is $$16x^2 - 40x - 25$$ where $$a=16$$, $$b=-40$$, and $$c=-25$$. 4. **Calculate product $$a \times c$$:** $$16 \times (-25) = -400$$. 5. **Find two numbers that multiply to $$-400$$ and add to $$-40$$:** These numbers are $$-50$$ and $$10$$ because $$-50 \times 10 = -400$$ and $$-50 + 10 = -40$$. 6. **Rewrite the middle term using these numbers:** $$16x^2 - 50x + 10x - 25$$. 7. **Group terms:** $$(16x^2 - 50x) + (10x - 25)$$. 8. **Factor each group:** $$2x(8x - 25) + 5(2x - 5)$$. 9. **Notice the binomials are not the same, so check carefully:** Actually, the second group factors as $$5(2x - 5)$$, but the first group factors as $$2x(8x - 25)$$, which are different. 10. **Since the binomials differ, try factoring by grouping differently or check for a common factor:** The original quadratic is not factorable by simple grouping, so let's try factoring the quadratic directly. 11. **Try factoring the quadratic $$16x^2 - 40x - 25$$ as $$(ax + b)(cx + d)$$:** - The product $$ac = 16$$. - The product $$bd = -25$$. - The sum $$ad + bc = -40$$. 12. **Possible factor pairs for 16:** (16,1), (8,2), (4,4). 13. **Possible factor pairs for -25:** (25,-1), (5,-5), (-25,1), (-5,5). 14. **Test combinations:** - Try $$(4x + 5)(4x - 5) = 16x^2 - 20x + 20x - 25 = 16x^2 + 0x - 25$$ (no). - Try $$(8x + 5)(2x - 5) = 16x^2 - 40x + 10x - 25 = 16x^2 - 30x - 25$$ (no). - Try $$(8x - 5)(2x + 5) = 16x^2 + 40x - 10x - 25 = 16x^2 + 30x - 25$$ (no). - Try $$(4x - 5)(4x + 5)$$ same as above. 15. **Try $$(8x - 10)(2x + 5)$$ but this is not in the form $$(ax + b)(cx + d)$$ with integer constants. 16. **Since the quadratic is not factorable over integers, the MT Test Method shows no integer factors.** 17. **Therefore, the factored form is simply:** $$-2x(16x^2 - 40x - 25)$$ or factor out $$-2x$$ as given. **Final answer:** $$-2x(16x^2 - 40x - 25)$$ cannot be factored further using the MT Test Method with integer factors.