c must be 8 so that we get 8x^2 when the factors are multiplied.
Also, ab=15 which gives us factors 1 and 15, 3 and 5, -1 and -15, -3 and -5. We choose the negative factors because of the minus in the middle term. Expansion of (x+a)(cx+b)=cx^2+x(b+ac)+ab. So b+8a=-121. 8*15=120, so a=-15 and b=-1. We have therefore (x-15)(8x-1) as the factorisation.