Final answer:
The characteristic of the sputum that supports the nurse's suspicion of a pulmonary embolus is coughing up blood (hemoptysis).
Step-by-step explanation:
The characteristic of the sputum that supports the nurse's suspicion that the client has a pulmonary embolus is a) hemoptysis (coughing up blood).
A pulmonary embolus is a blood clot that blocks a pulmonary artery in the lungs. Coughing up blood, known as hemoptysis, can occur when the blood clot disrupts the normal blood flow in the lungs and causes damage to the blood vessels, leading to bleeding.