Learn Russian: Этот признак кажется важным фактором. - This sign seems to be an important factor.

The verb казаться (to seem) requires the Instrumental case for the noun or adjective that describes the subject. It shows what the subject seems to be. Because фактор is a masculine noun, it takes the -ом ending, and the adjective важный takes the matching -ым ending.

Is кажется related to the verb for "to say"?

Yes! It shares a root with сказать (to say). You can think of казаться as something "presenting itself" or "being told" a certain way. Also, notice the consonant change in the present tense: the з becomes a ж (я кажусь, ты кажешься, он/она кажется).

If I want to say "a street sign", can I use признак?

No, признак refers to a sign in the sense of a feature, characteristic, symptom, or indication. If you are talking about a physical sign you see on the street, you would use знак (like a traffic sign) or вывеска (like a shop sign).

What if I drop the noun and just want to say "This sign seems important"?

You must still use the Instrumental case for the adjective. You would simply drop the noun and say Этот признак кажется важным.