Can someone help me on a math problem asap!?

Question

Given the function f(x) = 3x^3-10x^2+7x+10
Write f(x) as a product of linear factors.
Ok so this is what I have done so far:
P: +-1, +-2, +-5,+-10
Q: +-1, +-3
P/Q = +-1,+-2,+-5,+-10, +-1/3, +- 2/3, +-5/3, +-10/3

On the calculator I pressed 2nd trace and value and found that when x= -2/3, y=0. So that has to be one zero for sure. Just to make sure it was, I used synthetic division and the remainder was zero.
-2/3 / 3 -10 7 10
___-2_ 8_-10____
3 -12 15 -10
so I brought the equation down
3x^2-12x-15
factored: 3(x-5)(x+1)
x= 5, x = -1
Now this is where I am stuck..when I graphed the first equation..it only had one zero....which was -2/3
Now how do I write f(x) as a product of linear factors
So basically writing the same equation as given in a different form with all zeros.
Can someone help me please?
Thanks.

Answer 1

You used

3x^2-12x-15

when your synthetic division correctly gave

3x^2-12x+15

and other than the factor of 3, 3x^2-12x+15 can't be further factored (over the real numbers, anyway). So that's why your graph showed only one zero.

Answer 2

So your linear factors are 3(x + 2/3) (x - 2 +i)(x - 2 - i)