The completed sentence is: “He bade them welcome to his house.”

Here’s why:

• A. welcomed: This option is incorrect because “welcomed” is the past tense of “welcome” and doesn’t fit grammatically in this sentence.

• B. are welcome: This option is incorrect because “are welcome” is present tense and doesn’t fit with the past tense verb “bade”.

• C. to be welcome: This option is incorrect because it changes the meaning of the sentence and makes it less direct.

• D. to have been welcome: This option is incorrect because it changes the tense of the sentence and makes it overly complicated.

• E. welcome: This is the correct option. The word “bade” is an old-fashioned term for “asked” or “invited”, so “He bade them welcome” means “He invited them to be welcome”. It’s a more formal and old-fashioned way of saying “He welcomed them”.