The answer if the equation is changed to `+kx^2` changes to a negative answer. Thus:

81 +27 +9k +39+2 = 625 -125 +25k -65 + 2

`therefore` **k= - 18**

`(x^4 - x^3- kx^2 - 13x + 2)/ (x+3)` = R

`(x^4 - x^3 - kx^2 - 13x + 2)/(x+5)` =R

This means that when x=-3 (from x-3)AND when x=5 (from x+5) we have the same remainder. Substitute ,thus:

`(-3)^4 -(-3)^3-k(-3)^2-13(-3)+2=(5)^4-(5)^3-k(5)^2-13(5)+2`

They equal each other because R=R

81-(-27)-9k -(-39)+2=625 -125-25k-65+2

Care with the negative symbols:

81+27-9k+39+2= 437-25k

`therefore` 149 - 9k= 437 -25k

`therefore` -9k+25k = 437-149

`therefore` 16k=288

`therefore` **k=18**