Extemporize

01 v. i. To speak extempore; especially, to discourse without special preparation; to make an offhand address.

imp. & p. p. Extemporized; p. pr. & vb. n. Extemporizing

1.
To speak extempore; especially, to discourse without special preparation; to make an offhand address.

02 v. t. To do, make, or utter extempore or off-hand; to prepare in great haste, under urgent necessity, or with scanty or unsuitable materials; as,…

1.
To do, make, or utter extempore or off-hand; to prepare in great haste, under urgent necessity, or with scanty or unsuitable materials; as, to extemporize a dinner, a costume, etc.
“Themistocles . . . was of all men the best able to extemporize the right thing to be done.” — Jowett (Thucyd. ).

“Pitt, of whom it was said that he could extemporize a Queen's speech” — Lord Campbell.