Concept:To factor a quadratic x2−17x−38, find two numbers whose product is −38 and sum is −17. Those numbers are −19 and +2.Explanation:Rewrite the middle term −17x as −19x+2x.So x2−17x−38=x2−19x+2x−38.Group terms: (x2−19x)+(2x−38).Factor each group: x(x−19)+2(x−19).Now take common factor (x−19): (x−19)(x+2).Thus the factorised form is (x−19)(x+2).Answer:Option D: (x−19)(x+2)