Question about usage of 「のでは」

Question

In one of the grammar questions for N3, I saw one for which I couldn't understand the reason why のでは is used.

この英会話講師のアルバイトに応募したきっかけは、先輩からの紹介です。私の専門は言語学ですので、その知識が生かせる「　」、と思い、応募いたしました。文法に詳しいので、英語はもちろん、日本語での文法の説明もできます。

Possible answers are

1) から　２）とか　３）なんて　４）のでは

The answer marked as correct is のでは. However, I don't understand why. I know that のでは　is used in sentences like のではない。However, that's not he case here.　Also as ので、when implying reason. However in that case I don't see は added. When searching through google I found more cases where you can use like this "一歩間違えば指先に刺さるのではと思ってしまう".

However, I don't understand which grammar rule allows for this usage of のでは。

Answer 1

You are close. The omitted phrase is その知識が生かせるのではないか, where か is the question marking particle you must know well.

It says "Can't I make use of the knowledge? (I can!)" rather than saying "I can't make use of the knowledge".

Similarly, 刺さるのでは in that context means 刺さるのではない（だろう）か, meaning "I wonder if it pricks".

Answer 2

The "のでは" here implies it's one's (humble) opinion or suspicion.

One can also say "その知識が生かせるかと思い".

I presume this usage is related to "のではない".

Answer 3

のでは describes possibility.

私の専門は言語学ですので、その知識が生かせる「　」、と思い、応募いたしました。

I applied this opportunity because my proficient is Linguistics.
It's possible to take advantage of my knowledge.

Japan's Cultural expression way, we do not insist directly.
If this is English,
I am sure that I can take advantage of my skills in this field.
In Japan, we softly insist , that's why のでは is added.
のでは have effect to make the things more softly.

私の専門は言語学ですので、その知識が生かせると思い、応募いたしました。

In gramatical,
This sentence is also collect ,perfectly works.
You can use when you want to approach strongly.