WAEC Further Mathematics 2017 Paper

Concept:If one factor of a polynomial is known, the other factor can be found by comparing coefficients after multiplying the two factors.Explanation:Let the other factor be $(ax + b)$, since $f(x)$ is a cubic polynomial and the given factor is quadratic.Thus, $(2x^{2} - x - 3)(ax + b) = 2x^{3} - 5x^{2} - x + 6$.Compare the leading coefficients: $2a = 2$, so $a = 1$.Compare the constant terms: $-3b = 6$, so $b = -2$.Hence, the other factor is $(x - 2)$.Verification: $(2x^{2} - x - 3)(x - 2) = 2x^{3} - 5x^{2} - x + 6$, which equals $f(x)$.Therefore, the missing factor is $(x - 2)$.Answer:Option A: $(x - 2)$