Choose the correct phrase to complete the food critic's scathing restaurant review.

The notorious head chef of The Greasy Spoon is rumored _____ a single fresh vegetable in his entire twenty-year career.

The correct answer is not to have cooked.

When making a passive reporting infinitive negative, we place not immediately before to (e.g., not to have cooked).

Because the sentence refers to a completed period covering his past experience ("his entire twenty-year career"), we must use the perfect infinitive (have cooked) rather than the simple infinitive (cook). "That he hasn't cooked" is grammatically incorrect here because it lacks the dummy subject "It" (e.g., It is rumored that he hasn't cooked...).