x^4-x^3-6x^2+4x+8 what kind of substitution was used to get the real zeros

Question

I came up with the real zeros are -2,-1 and 2  and put the use of synthetic division, but I can't find how I did this. - any ideas?

Answer 1

I would have done the same thing synthetic division or long divison.  I would try the multiples of

8 = 1, 2, 4, 8 plus or minus versions.

try (x+2)

2   |  1       -1      -6        4        8

     |            2        2       -8      -8

     ------------------------------------

        1        1       -4       -4      0

so (x + 2)(x^3 - 4x^2 - 4x)

factor out an x

x(x + 2)(x^2 - 4x - 4)

x(x + 2)(x +2)(x - 2) set = 0

x = 0 or x = -2 or x = 2

-1 is not a root 0 is...

Comments

this is what happens when you throw away the scrap of paper you did your figuring on - you forget how you derived the answer  - thanks