we have the function
f(x)=x^4-x^3-7x^2+45x-39
Find out f(-5)
so
Use synthetic division
x^4-x^3-7x^2+45x-39 : (x+5)
x^3-6x^2+23x-70
-x^4-5x^3
-------------------------------
-6x^3-7x^2+45x-39
6x^3+30x^2
----------------------------
23x^2+45x-39
-23x^2-115x
------------------------
-70x-39
70x+350
------------------
311 ----------------> remainder
therefore
f(-5)=311
Verify
using a graphing tool
For x=-5 ------------> f(x)=311 is ok