Find a polynomial with real coefficients and the zero's -1, 5-4i

one such polynomial P(x) can be defined as P(x)=x^3-9x^2+_x+41

help me find the "_" please?

Question

Find a polynomial with real coefficients and the zero's -1, 5-4i

one such polynomial P(x) can be defined as P(x)=x^3-9x^2+_x+41

help me find the "_" please?

dumbcow · Answer

Divide out the (x+1) using synthetic division
-1| 1      -9        a        41
               -1      10   -(a+10)
   -------------------------
      1     -10      (a+10)     0
Then conclude that 
a +10 = 41
a = 31