f(x) = kx^3+5x^2-7kx-8
if x-k is a factor, x=k
f(k) = k^4+5k^2-7k^2-8 = 0
k^4 - 2k^2 -8
= 0
(k^2-4)(k^2+2) =0
k^2 = 4 or k^2 = -2 (rejected)
taking sqroot 4,
k = 2 or k = -2 (rejected as k is +ve integer)
*note tt square root always have + and - ans.
f(x) = 2x^3+5x^2-14x-8=0
use long division to find other factor
f(x) = (x-2)(2x^2+9x+4)
= (x-2)(2x+1)(x+4)