Without using a calculator find all the roots of the following equation. x cubed plus x squared -17 x +15 equals zero

I wonder if you could graph it? Just in case you can, I'll include that.
You could try 1 in the original equation
x^3 + x^2 - 17x + 15 = y If it equals 0 when you put 1 in, then that is a solution.
1 + 1 - 17 + 15 and it does = 0. 
One factor is (x - 1) <<<< answer 1
Notice that the sign changes. The reason for that is you want to put 1 in for the x and have the result  of x - 1 = 0. 

Now we could try - 1 to see if it will turn the original equation into 0. It might.
x^3 + x^2 - 17x + 15 = y
(-1)^3 (-1)^2 - 17(-1) + 15 which not going to equal 0 because 17 becomes a plus.

At this point, we could do a division

x - 1 || x^3 + x^2 - 17x + 15 || x^2 + 2x - 15
           x^3 - x^2 
          ========
                    2x^2 - 17x
                    2x^2 -   2x
                    ========
                             - 15x + 15
                             - 15x + 15
                                =======
                                         0

 we now need to factor x^2 + 2x - 15 which factors easily into
(x + 5)(x - 3)=y1
x + 5 = 0
x = - 5
x - 3 = 0
x = 3
So the three roots are 1,3,-5 <<< answer. Look ma, no calculator and as promised, a graph to confirm.
The factors are y = (x - 1)(x - 3)(x + 5)

Polar coordinates is 8,9