Which is the correct factorised form of (2x^2-7x+3)?

Correct answer: ((2x-1)(x-3))

The direct answer is option A:
\((2x-1)(x-3)\). To factorise, we look for two binomials whose first terms multiply to \(2x^2\), whose constant terms multiply to \(3\), and whose middle terms add to \(-7x\). Expand A step by step: \((2x-1)(x-3)=2x^2-6x-x+3=2x^2-7x+3\), so it matches exactly. Option A is correct because all three terms agree. Option B gives \((2x+1)(x-3)=2x^2-5x-3\), so both the middle and constant terms differ. Option C gives \((2x-3)(x-1)=2x^2-5x+3\), so the middle coefficient is wrong. Option D gives \((x-1)(x-3)=x^2-4x+3\), so even the coefficient of \(x^2\) is wrong. A useful exam cue is to expand every proposed factorisation and compare all three terms, not only the first and last terms.