2021 RI Promo Q5

Using standard series from the List of Formulae (MF26), expand \(\frac{\cos 3x}{4-x}\) as far as the term in \({{x}^{3}}\). Give the coefficients as exact fractions in their simplest form.[4]

It is given that the third and fourth terms found in part (i) are equal to the third and fourth terms in the series expansion of \({{\left( a+bx \right)}^{5}}\), in ascending powers of \(x\) respectively. Find the values of the constants \(a\) and \(b\).[4]