(a) Express \(f(x)\) in partial fractions:

Assume \(\frac{21 - 8x - 2x^2}{(1 + 2x)(3 - x)^2} = \frac{A}{1 + 2x} + \frac{B}{3 - x} + \frac{C}{(3 - x)^2}\).

Find constants \(A, B, C\) by equating coefficients:

\(A = 2, \ B = 2, \ C = -3\).

(b) Expand each partial fraction:

\(\frac{2}{1 + 2x} = 2(1 - 2x + 4x^2 + \ldots)\)

\(\frac{2}{3 - x} = \frac{2}{3}(1 + \frac{x}{3} + \frac{x^2}{9} + \ldots)\)

\(\frac{-3}{(3 - x)^2} = -\frac{1}{3^2}(1 + \frac{2x}{3} + \frac{3x^2}{9} + \ldots)\)

Combine and simplify terms up to \(x^2\):

\(f(x) = \frac{7}{3} - 4x + \frac{215}{27}x^2\).