Answer: D
$5(9x^2 - 4) = 5(3x-2)(3x+2)$, giving zeroes $x = \dfrac{2}{3}$ and $x = -\dfrac{2}{3}$. ✓
Source: Chapter 2, Section 2.3
To find the correct option, check which polynomial gives zeroes $\frac{2}{3}$ and $-\frac{2}{3}$. The required polynomial is of the form $k(x - \frac{2}{3})(x + \frac{2}{3}) = k(x^2 - \frac{4}{9})$. Option D: $5(9x^2 - 4) = 45(x^2 - \frac{4}{9})$, which matches. Option A ($4x^2 - 9$) gives zeroes $\pm\frac{3}{2}$, not $\pm\frac{2}{3}$. Always substitute the zeroes or factorise to verify quickly.