Factorise $y^2 -3yz -10z^2$ How do I solve this question? I have looked at the problem several times. However, I cannot find a viable solution. I believe that it is a perfect square trinomial problem. 

As Andre pointed, you can guess the factors by inspection.
Alternately, we can factor $z^2$ and then you get
$$z^2[(\frac{y}{z})^2-3 \frac{y}{z}-10] \,.$$
Denoting $\frac{y}{z}=w$ the problem reduces to factoring 
$$w^2-3w-10$$
This can be factored as $(w-a)(w-b)$ where $a,b$ are the two roots of $w^2-3w-10=0$.
Calculate the roots, and remultiply by $z^2$ to get the factorization.
