Question

Factorise: $\frac{1}{3}{x}^2-2x-9$

Answer 1

The given expression is $\frac{1}{3}{x}^2-2x-9$.

The expression can be factorised as follows:

$\frac{1}{3}{x}^2-2x-9=\frac{x^2-6x-27}{3}=\frac{1}{3}(x^2-6x-27)=\frac{1}{3}(x^2-9x+3x-27)=\frac{1}{3}\left[x\right(x-9)+3(x-9\left)\right)=\frac{1}{3}(x-9)(x+3)$

Hence, $\frac{1}{3}{x}^2-2x-9=\frac{1}{3}(x-9)(x+3)$