Mathematics Past Questions and Answers

Find the coefficient of \(x^{3}\) in the expansion of \([\frac{1}{3}(2 + x)]^{6}\).

If \(y = 4x - 1\), list the range of the domain \({-2 \leq x \leq 2}\), where x is an integer.

Factorize completely: \(x^{2} + x^{2}y + 3x - 10y + 3xy - 10\).

If the solution set of \(x^{2} + kx - 5 = 0\) is (-1, 5), find the value of k.

The remainder when \(x^{3} - 2x + m\) is divided by \(x - 1\) is equal to the remainder when \(2x^{3} + x - m\) is divided by \(2x + 1\). Find the value of m.