Factor the trinomial. \[ v^{2}-15 v+56 \]

Step 1 ：The expression \(v^{2}-15 v+56\) is in the form \(Ax^2+Bx+C\). We need to find two integers \(a\) and \(b\) such that \(a+b=B=-15\) and \(ab=AC= (1)(56)=56\).

Step 2 ：We find that \(a=-7\) and \(b=-8\) satisfy these conditions, since \(-7+(-8)=-15\) and \((-7)(-8)=56\).

Step 3 ：Next, we can use these values to rewrite the \(v\)-term and factor by grouping.

Step 4 ：\(v^{2}-15 v+56=v^{2}-7v-8v+56\)

Step 5 ：\(v^{2}-15 v+56=v(v-7)-8(v-7)\)

Step 6 ：In conclusion, \(v^{2}-15 v+56=(v-8)(v-7)\)

Step 7 ：So, the final answer is \(\boxed{(v-8)(v-7)}\)