Quite means "to a considerable extent or degree."

This is quite interesting.

Much can also mean "to a great extent or degree," and far can mean "much," but you can't always replace one word with another.

You can use "much" or "far" before comparative adjectives (Macmillan Dictionary). You make "interesting" a comparative adjective by saying "more interesting." So you can say:

This is much (or far) more interesting.

Quite means "to a considerable extent or degree."

This is quite interesting.

Much can also mean "to a great extent or degree," and far can mean "much," but you can't always just replace one word with another.

We do not use "much" or "far" before adjectives in their positive forms (interesting, quick...) but only before their comparative forms (more interesting, quicker...) (Macmillan Dictionary). So you can say:

This is much (or far) more interesting.

Quite means to a considerable extent or degree.

This is quite interesting.

Much can also mean "to a great extent or degree," and far can mean "much," but you can't always replace one word with another.

In your context, you can use "much" or "far" only together with "more," which makes "more interesting" a comparative adjective.

This is much (far) more interesting.

In general, we do not use "much" or "far" before adjectives. So you can't say "much interesting" or "far interesting." It can help you if you think that "much" and "far" do not mean "very."

Quite means "to a considerable extent or degree."

This is quite interesting.

Much can also mean "to a great extent or degree," and far can mean "much," but you can't always replace one word with another.

You can use "much" or "far" before comparative adjectives (Macmillan Dictionary). You make "interesting" a comparative adjective by saying "more interesting." So you can say:

This is much (or far) more interesting.