When given a factor (such as x + 2), set it equal to zero.

Then we will have x = -2. This is the number that goes "in the box" when doing synthetic division.

There's no way I'm going to try to visually reproduce the process (!), so I'll just talk you through it...

Your coefficients are 3, -4, -17, and 6.

Bring down the

3. Then 3*-2 + -4 =

-10. Then -10*-2 + -17 =

3. Then 3*-2 + 6 = 0 (as it should).

You now have coefficients 3, -10, and 3, corresponding to the quadratic

Now you can factor this into (3x - 1)(x - 3), but don't lose the original factor!

Your full factorization is (3x - 1)(x - 3)(x + 2)