If \(f(x) = 6x^{3} + 13x^{2} + 2x - 5\) and \(f(-1) = 0\), find the factors of f(x).

If \(\alpha\) and \(\beta\) are the roots of the equation \(2x^{2} - 7x + 4 = 0\), find the equation whose roots are \(\frac{\alpha}{\beta}\) and \(\frac{\beta}{\alpha}\).

(a) Write down the binomial expansion of \((2 - x)^{5}\) in ascending powers of x.

(b) Use your expansion in (a) to evaluate \((1.98)^{5}\) correct to four decimal places.

Solve \(2^{(2y + 2)} - 9(2^{y}) = -2\).

(a) Write the following as column vectors: \(r = (10N, 090°) ; q = (8N, 135°)\).

(b) Use your answer in (a) to find \((r + q)\).