Concept:The Remainder Theorem states that if f(x) is divided by (x−a), the remainder is f(a).Here, the divisor is (x−4), so we evaluate f(4).Explanation:Given f(x)=5x3+7x2−4x+9.Substitute x=4 into f(x):f(4)=5(4)3+7(4)2−4(4)+9=5(64)+7(16)−16+9=320+112−16+9=425.So the remainder when f(x) is divided by (x−4) is 425.Answer:425, which is option D.