In the following question, a sentence is given with a bracketed part that may contain an error. Choose the alternative that will best replace the bracketed part. In case no improvement is needed, select the option no improvement. Why should we (bothered)?

Introduction / Context:
This question checks knowledge of correct verb forms after modal auxiliaries in English grammar. The sentence uses the modal verb should, and the bracketed word must be adjusted to match the required structure. Mastery of bare infinitives after modals such as can, could, may, might, shall, should, will, and would is essential for error spotting questions in competitive exams.

Given Data / Assumptions:

• Sentence: Why should we (bothered)?
• Options: bother, bothering, to bother, no improvement.
• The auxiliary verb in the sentence is should.
• We assume standard modern English grammar rules for modal verbs.

Concept / Approach:
Modal auxiliaries such as should are followed by the base form of the main verb, also called the bare infinitive. We say should go, should study, should help, not should to go or should going. The word bothered is a past participle or simple past form, so it is incorrect here. The correct base form is bother. The approach is to identify the modal and then choose the bare infinitive that agrees with it, ensuring that the structure aligns with standard patterns like Why should we bother.

Step-by-Step Solution:
Step 1: Identify the modal auxiliary in the sentence. The word should is a modal.Step 2: Recall the rule that modals are followed by the bare infinitive, without to and without -ing or -ed endings.Step 3: List the bare infinitive of the verb in question. The main verb is bother, so the base form is bother.Step 4: Replace the bracketed word with each option: should we bother, should we bothering, should we to bother, should we bothered. Only should we bother is grammatically correct and natural.Step 5: Therefore, the correct improvement is to choose bother as the replacement for bothered.

Verification / Alternative check:
You can verify the structure by comparing with other familiar sentences: Why should we worry, Why should we care, Why should we try. In each case, the verb after should is in its base form. Also, if we rewrite the sentence without the modal, we can say We are bothered, but that is a different tense and meaning. In the question form with should, the only acceptable pattern is should plus bare infinitive, confirming that bother is correct.

Why Other Options Are Wrong:
Bothering: This is a present participle and would require an auxiliary such as are if it were to be used, as in Why are we bothering. It cannot directly follow should. To bother: The structure should to bother is incorrect because modals do not take to before the next verb. No improvement: Keeping bothered would keep the sentence ungrammatical because should we bothered is not a correct combination in this context. Therefore all three alternatives are unacceptable.

Common Pitfalls:
Students sometimes confuse the patterns used with ordinary auxiliaries and modal auxiliaries. For example, they know forms like are bothering or were bothered and then mistakenly extend similar forms after should. Another pitfall is to think that to must follow every auxiliary, which is not true for modals. The safest strategy is to memorise that can, could, may, might, shall, should, will, would, must, and ought to (special case) are followed directly by the base form of the main verb, without additional markers, except for ought to which already contains to inside the modal phrase itself.

Final Answer:
The correct replacement for the bracketed part is bother, so the sentence reads, Why should we bother.