Answer:
k = - 14
Explanation:
By the remainder theorem
if a function f(x) is divided by (x - a) then the remainder is f(a)
given a remainder of zero when divided by (x - 5) , then
substituting x = 5 into the polynomial and equating to zero
x³ - x² + kx - 30 , gives
5³ - 5² + 5k - 30 = 0
125 - 25 + 5k - 30 = 0
5k + 70 = 0 ( subtract 70 from both sides )
5k = - 70 ( divide both sides by 5 )
k = - 14