The negative form of い-Adjectives in Japanese is created by using the conjunctive form of the adjective, followed by ない. Conjunctive form just means 'agglutinative', or 'conjunctive' in Japanese. For い-Adjectives, this conjunctive form is created by removing い, and replacing it with く.

The ない used with い-Adjectives is considered to be a different word to the ない used with verbs. When used with い-Adjectives, ない itself is also an い-Adjective. This means that it follows the same rules as regular い-Adjectives. Due to ません (the polite negative form) being an auxiliary verb, it cannot be conjugated with い-Adjectives in the same way as verbs.

As can be seen here, you must first add the verb ある, and then conjugate it into its negative form using the auxiliary verb ません. This is how the polite negative is created.