How do you factor by grouping this.

What in the world is ^ that sign?

Princess means this:

6v^{\text{3}}-16v^{\text{2}}+21v-56

Well, I had some trouble with that. It's a trial and error method.

If f(v) = 6v^3 - 16v^2 + 21v - 56

Then, if (v-a) is a factor of f(v), then f(a) = 0.

So, you have to find the value of a for which f(a) = 0.

I tried f(1), giving f(1) = 6(1)^3 - 16(1)^2 + 21(1) - 56 = -45.

So, (v - 1) is not a factor.

I won't show everything I tried, it would be a mess, but I got (v - 8/3)

Check:

f(\frac83) = 6(\frac83)^3 - 16(\frac83)^2 + 21(\frac83) - 56 = 0

So, (3v - 8) is a factor of f(v).

Now, you can divide (6v^3 - 16v^2 + 21v - 56) by (3v - 8)