One of the factors of (mn - nq - n$^2$ + mq) is (m - n). The other factor is?

Let me work through this carefully.

Step 1: Analyze the question We need to factorise mn − nq − n² + mq and find the factor that goes with (m − n).

Step 2: Group the terms Rearrange the expression so that terms with common factors sit together:

mn − n² + mq − nq

Step 3: Factorise each group

• mn − n² = n(m − n)
• mq − nq = q(m − n)

Step 4: Take out the common factor n(m − n) + q(m − n) = (m − n)(n + q)

Step 5: Check by expanding (m − n)(n + q) = mn + mq − n² − nq

This matches the original expression, mn − nq − n² + mq.

Answer: The other factor is (n + q), which is option C.

Exam tip: When you see a four-term expression, try factorisation by grouping. Pair the terms so each pair has a common factor, and the same bracket should appear in both pairs. If it does, you are on the right track. Always expand your answer quickly to check it.