Find all the real zeros of the polynomial

Question

find all the real zeros of the polynomial

P(x)=x⁴-2x³-13x²-10x

If there is more than one zero write them separated by commas. Give EXACT answers. No decimals.

Answer 1

x^4-2x^3-13x^2-10x

using synthetic division

 

             1       -2       -13       -10

  -2                 -2         8          10

             1       -4        -5            0

 

 

              1       -4       -5     

 

   -1                 -1        5

              1       -5        0

 

 

              1       -5

 

     5                 5

              1        0

 

solution: (x+2)(x+1)(x-5)x = x^4-2x^3-13x^2-10x

x= -2, x= -1, x= 5, x=0