1. The problem is to verify the factorization of the quadratic expression $$2x^2 - 13x + 20$$ given as $$(2x - 5)(x - 4)$$. 2. The formula for expanding two binomials is: $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. Applying this to $$(2x - 5)(x - 4)$$: $$ 2x \cdot x + 2x \cdot (-4) + (-5) \cdot x + (-5) \cdot (-4) $$ 4. Simplify each term: $$ 2x^2 - 8x - 5x + 20 $$ 5. Combine like terms: $$ 2x^2 - 13x + 20 $$ 6. This matches the original quadratic expression, so the factorization is correct.