JAMB Mathematics 2014 Paper

Concept:Factorization of a quadratic expression by splitting the middle term.Explanation:We are to factorize $2y^{2} - 15xy + 18x^{2}$.Multiply the coefficient of $y^{2}$ by the constant term: $2 \times 18x^{2} = 36x^{2}$.Find two terms whose product is $36x^{2}$ and whose sum is $-15xy$.The required terms are $-12xy$ and $-3xy$ because $(-12xy)(-3xy) = 36x^{2}y^{2}$ and $-12xy - 3xy = -15xy$.Rewrite the expression using these two terms:$2y^{2} - 12xy - 3xy + 18x^{2}$.Now factor by grouping:$2y(y - 6x) - 3x(y - 6x)$.Both groups contain the common factor $(y - 6x)$.Factor out $(y - 6x)$ to get:$(2y - 3x)(y - 6x)$.This matches the standard factorization of the given quadratic expression.Answer:$(2y - 3x)(y - 6x)$, which is option B.