Further Mathematics Past Questions and Answers

If \((x + 2)\) and \((3x - 1)\) are factors of \(6x^{3} + x^{2} - 19x + 6\), find the third factor.

If \(2, (k+1), 8,...\) form an exponential sequence (GP), find the values of k.

If \(\frac{1}{5^{-y}} = 25(5^{4-2y})\), find the value of y.

Simplify: \((1 - \sin \theta)(1 + \sin \theta)\).

Given that \(3x + 4y + 6 = 0\) and \(4x - by + 3 = 0\) are perpendicular, find the value of b.