'quite' in this case brings a feeling of unexpectedness, like 'wow!'. normally, in front of adjectives is means 'pretty/fairly/to some extent' (less than 'very)

Wow! What a difficult question this is to answer. Both of the sentences are correct but the difference in employing the word 'quite' is a nuance added for either a positive or negative reaction to the speech which is dependent on the tone used. Applying either a negative or positive tone to the word 'quite' will indicate whether the speaker was impressed by the speech or not. More usually, in English usage "It was quite a remarkable speech" would indicate a positive endorsement of what has been said.

Hi Mammar, yes it is definitely correct to say "it was a remarkable speech."

1. All hell broke loose= a lot of trouble started. "After I yelled "Your momma is ugly" at the gang leader, all hell broke loose, and 15 different gang members all tried to punch me at once." Adding "would" can either make it conditional or "future in the past" Conditional: I really want to insult that gang leader's mother, but I know that if I insulted her, all hell would break loose, so I won't insult her. Future in the past: Yesterday, I decided to insult the gang leader's mother, but I knew that, after I insulted her, all hell would break loose, so I planned my escape route before saying anything. 2. When "quite" is in front of an adjective, it means "very" He was quite angry= he was very angry. When it is in front of a noun, it means "real" or "true" He is quite a scholar= he is more scholarly than most scholars are If you say "not quite", it means "slightly less than the minimum" I'm not quite finished writing this essay= I still have to write the last few sentences. So yes, you can say "it was a remarkable speech." If you say "quite remarkable," it wil make the speech even more remarkable.