The possible rational roots are 1, -1, 5, -5, 1/2, -1/2, 5/2, and -5/2.
You could test each possible root using synthetic division, but that would be a long slow process. Checking for zeros (roots) by evaluating the polynomial for each root is faster.
x=1: 2+8-11-5 = -6 --> not a root
x=-1: -2+8+11-5 = 12 --> not a root
x=5: 250+200-55-5 = 490 --> not a root
x=-5: -250+200+55-5 = 0 --> -5 is a root
Divide the polynomial by (x-(-5)) to find the remaining quadratic polynomial.
-5 | 2 8 -11 -5
| -10 10 5
+---------------
2 -2 -1 0
This tells us that
The quadratic factor is not factorable over the integers; find the other two roots using the quadratic formula. The other two (irrational) roots are
ANSWERS: ,,