Hello Caron!

Factor: \(\displaystyle \L v^2\, -\, 22v\, -\, 75\)

Ok since we have \(\displaystyle v^2\) in our polynomial we need to think: What are two numbers that multiply to give us -75 and add up to -22? So after playing w/this a little bit you arrive at -25 and 3. Notice: 25 * -3 = -75 and -25 + (3) = -22. If we could not find these two number then we could just use the Quadratic Formula since I doubt you have learned difference of squares. Ok?

So since 3 > -25 our answer is:

\(\displaystyle \;\;\;\L (v+3) (v-25)\)

Check by FOIL:

\(\displaystyle \L \;\;\;v^2-25v+3v-75\,\to\,v^2\,-\,22v\,-\,75\)

Hope this helps.