Mam dobrą wiedzę ogólną.

Because mam already means I have. It is the 1st person singular form of mieć (to have).

Polish usually drops subject pronouns when they are not needed, because the verb ending already shows who is doing the action. So:

• Mam dobrą wiedzę ogólną. = I have good general knowledge.
• Ja mam dobrą wiedzę ogólną. is also possible, but ja adds emphasis, like I do have good general knowledge.

Polish does not have articles, so there is no direct equivalent of a/an/the.

That means wiedzę can be understood from context. In natural English, this sentence is usually translated as I have good general knowledge, not I have a good general knowledge, because knowledge is normally uncountable in English.

Because after mam (I have), the thing you have is a direct object, and in Polish that usually takes the accusative case.

The basic dictionary forms are:

• dobra = good
• wiedza = knowledge
• ogólna = general

But in the accusative singular feminine, they become:

• dobrą
• wiedzę
• ogólną

So:

• dobra wiedza ogólna = nominative
• mam dobrą wiedzę ogólną = accusative after mam

Wiedza is a feminine noun. That matters because adjectives in Polish must agree with the noun in:

• gender
• number
• case

So since wiedzę is feminine, singular, accusative, both adjectives also have to be feminine, singular, accusative:

• dobrą
• ogólną

In Polish, adjectives often come before the noun, but some expressions are commonly used with the adjective after the noun.

Wiedza ogólna is a very common set phrase meaning general knowledge. Because of that, in this sentence you get:

• wiedzę ogólną

rather than only:

• ogólną wiedzę

Both are possible, but wiedza ogólna sounds like a more established term, almost like the category general knowledge.

Yes, both are grammatical.

• Mam ogólną wiedzę. = I have general knowledge.
• Mam dobrą ogólną wiedzę. = I have good general knowledge.

The original Mam dobrą wiedzę ogólną keeps the common phrase wiedza ogólna together, so it can sound a little more formal or fixed.

Yes, literally it means good, but in this kind of sentence it often means something like:

• solid
• fairly strong
• quite good

So it is not just moral good; it describes the quality or level of your knowledge.

Because Polish divides English know into different ideas:

• wiem = I know a fact
• znam = I know / am familiar with a person, place, book, topic, etc.
• mam wiedzę = I have knowledge

So this sentence is built around having knowledge, not simply knowing.

For example:

• Wiem, że to prawda. = I know that it is true.
• Znam ten temat. = I know this topic / I am familiar with this topic.
• Mam dobrą wiedzę ogólną. = I have good general knowledge.

Yes, it is natural, but it sounds a bit formal or self-evaluative. It fits contexts like:

• a job interview
• a CV
• a school or exam context
• describing your abilities

In casual conversation, someone might say something less formal, for example:

• Mam niezłą wiedzę ogólną. = I have pretty good general knowledge.
• Sporo wiem o różnych rzeczach. = I know quite a lot about different things.

A few useful points:

• w sounds like English v
• wi before a vowel sounds roughly like vy
• dz sounds like the ds in beds
• ą and ę are nasal vowels

So:

• wiedzę starts roughly vye-
• the dz is a clear consonant sound, not like English j
• final ę is often only lightly nasal in normal speech
• ą in dobrą and ogólną is also nasal

You do not need to overdo the nasal sound; a light, natural nasal quality is better than forcing it.

Yes. Polish word order is more flexible than English because endings show the grammatical role of words.

The most neutral version is:

• Mam dobrą wiedzę ogólną.

Other orders are possible for emphasis, but they sound more marked, for example:

• Dobrą wiedzę ogólną mam.

That is grammatical, but less neutral and more emphatic. For a learner, the original order is the safest one to use.