Factorise $x^{3}+2x^{2}-13x+10$.

(N/A) Let $p(x) = x^{3}+2x^{2}-13x+10$.
By the Factor Theorem,we test the factors of the constant term $10$ (i.e.,$\pm 1, \pm 2, \pm 5, \pm 10$).
For $x = 1$,$p(1) = (1)^{3} + 2(1)^{2} - 13(1) + 10 = 1 + 2 - 13 + 10 = 0$.
Since $p(1) = 0$,$(x-1)$ is a factor of $p(x)$.
Dividing $p(x)$ by $(x-1)$,we get $x^{2}(x-1) + 3x(x-1) - 10(x-1) = (x-1)(x^{2}+3x-10)$.
Now,factorise the quadratic expression $x^{2}+3x-10$ by splitting the middle term:
$x^{2} + 5x - 2x - 10 = x(x+5) - 2(x+5) = (x-2)(x+5)$.
Thus,the factors are $(x-1)(x-2)(x+5)$.