To factorise a trinomial x² + bx + c, whose leading coefficient is 1, in the form (x + p)(x + q), what relation must p and q satisfy?

Correct answer: p + q = b and pq = c

The direct answer is A: p + q = b and pq = c. Expand the proposed factors step by step: (x + p)(x + q) = x·x + x·q + p·x + p·q = x² + (p + q)x + pq. Now compare this with x² + bx + c. The coefficient of x must therefore satisfy p + q = b, and the constant term must satisfy pq = c. Option B reverses these roles, so it would give the wrong coefficient and constant term. Option C uses a difference that does not appear in the expansion and gives no correct product condition. Option D unnecessarily assumes p and q are equal; many valid factorisations use different numbers, such as (x + 3)(x + 4). Memory cue: in a monic quadratic, the pair’s sum controls the middle coefficient and its product controls the constant term.