Factorise $: x^{3}-x^{2}-17 x-15$

(D) Let $p(x) = x^{3}-x^{2}-17 x-15$.
To find a factor,we test values using the Factor Theorem. Let us check $x = -1$:
$p(-1) = (-1)^{3} - (-1)^{2} - 17(-1) - 15 = -1 - 1 + 17 - 15 = 0$.
Since $p(-1) = 0$,$(x+1)$ is a factor of $p(x)$.
Now,we divide $p(x)$ by $(x+1)$ or split the terms:
$x^{3}-x^{2}-17 x-15 = x^{3}+x^{2}-2x^{2}-2x-15x-15$
$= x^{2}(x+1) - 2x(x+1) - 15(x+1)$
$= (x+1)(x^{2}-2x-15)$
Now,factorize the quadratic expression $(x^{2}-2x-15)$ by splitting the middle term:
$x^{2}-5x+3x-15 = x(x-5)+3(x-5) = (x-5)(x+3)$.
Thus,the factors are $(x+1)(x-5)(x+3)$.