Factorise : $2x^{3}-3x^{2}-17x+30$

(D) Let $f(x) = 2x^{3}-3x^{2}-17x+30$ be the given polynomial.
By testing values,we find $f(2) = 2(8) - 3(4) - 17(2) + 30 = 16 - 12 - 34 + 30 = 0$. Thus,$(x-2)$ is a factor.
By testing $f(-3) = 2(-27) - 3(9) - 17(-3) + 30 = -54 - 27 + 51 + 30 = 0$. Thus,$(x+3)$ is a factor.
Since $(x-2)$ and $(x+3)$ are factors,their product $(x-2)(x+3) = x^{2}+x-6$ is also a factor.
Dividing $2x^{3}-3x^{2}-17x+30$ by $(x^{2}+x-6)$:
$2x^{3}-3x^{2}-17x+30 = (x^{2}+x-6)(2x-5)$.
Further factoring $(x^{2}+x-6)$ into $(x-2)(x+3)$,we get:
$2x^{3}-3x^{2}-17x+30 = (x-2)(x+3)(2x-5)$.