Question 21889
f(x) = x^4 - x^3 - 2x^2 - 4x - 24 ...TRY ,F(0),F(10,F(-1),F(2)...ETC....WE NOTE THAT F(-2) IS ZERO SO X+2  IS A FACTOR...LET US DIVIDE WITH X+2 USING HORNERS SHORT DIVISION.PLEASE COME BACK IF YOU ARE NOT CONVERSANT WITH THIS DIVISION...

-2....|1....-1....-2....-4....-24...........................................
......|0....-2.....6....-8.....24............................................
-------------------------------------------------
......|1....-3.....4....-12.....0
HENCE QUOTIENT IS 
X^3-3X^2+4X-12......WE FIND THAT F(3) IS ZERO...SO X-3 IS A FACTOR..AGAIN DIVIDING 
WITH X-3 WE GET

3.....|1....-3.....4....-12.....
......|0....3......0.....12.....
--------------------------------------
......|1....0......4.....0
HENCE QUOTIENT IS 
X^2+4
=(X)^2-(2I)^2
=(X+2I)(X-2I)
HENCE COMPLETE FACTORISATION IS 

f(x) = x^4 - x^3 - 2x^2 - 4x - 24 .=(X+2)(X-3)(X+2I)(X-2I)...THE ROOTS OR X INTERCEPTS ARE ....-2,3,2I AND -2I