Algebra: Expansion, Factorisation & Equations

(a) Expand and simplify (2x − 3)(x + 5) − (x − 4)². [3] (b) Factorise completely 6xy − 9y + 4x − 6. [2] (c) Solve 2x² − 1x − 3 = 0. [2]

(a) Simplify (x² − 9) / (3x² + 12x + 9). [3] (b) Given that y = (5x − 2) / (x + 3), make x the subject of the formula. [3]

(a) Express y = x² − 4x − 10 in the form y = a(x + b)² + c, where a, b and c are constants. [3] (b) Hence state the coordinates of the turning point of the curve. [1]