Find all the zeros: x^4-2x^3-23x^2-2x-24

Answer 1

using synthetic division

-4 1 -2 -23 -2 -24

-4 24 -4 24

1 -6 1 -6 0

This becomes x³ - 6x² + x -6 =0

Factor by grouping gives x²( x - 6 ) +1( x-6 )

(x² + 1) (x - 6 )=0

Set each of these = 0 to get

x = i, -i, 6 and don't forget 4 (the # you used for synthetic division)