How do I use synthetic division to figure out the solution?

Question

Use synthetic division to show that the number given to the right of the equation is a solution of the equation, then solve the polynomial equation.

x³ - 5x² + 2x + 8 =  0; 2

Answer 1

2 | 1 -5 2 8

2 -6 -8

____________________

1 -3 -4 0

and

2^3 - 5(2^2) + 2(2) + 8 =

8 - 5*4 + 4 + 8 =

-12+4+8 = 0

so yes, x=2 is a solution because the remainder is zero

when divided by x-2

x^2-3x-4 = 0

( x - 4)(x + 1 ) = 0

x = 4 or x =-1 are the other two solutions