Mastering Algebra: From Factorisation to Quadratics

Algebra is the gateway to Mathematics success at WAEC, NECO, and JAMB. Students who struggle with it almost always have the same root problem: they skip steps when factorising, creating small errors that cascade into wrong answers. Let us fix that. Factorisation of quadratics: given ax² + bx + c = 0, find two numbers that multiply to ac and add to b. Example: 6x² + 11x + 4. Here a=6, c=4, so ac=24. We need two numbers that multiply to 24 and add to 11: they are 3 and 8. Rewrite: 6x² + 3x + 8x + 4, then factor by grouping: 3x(2x+1) + 4(2x+1) = (3x+4)(2x+1). The quadratic formula x = (−b ± √(b²−4ac)) / 2a works when factorisation is not obvious — and it always works. Completing the square is useful for deriving the vertex form of a parabola, which appears in coordinate geometry questions. Practise five factorisation problems daily for two weeks and the patterns become instinctive.