Answer: The value of k is 6
f(x)=x^3+kx^2+5x-3
Divided by x+5 gives a remainder of -3
If we replace in the polynomial f(x), x by (-5) we must get -3:
x=-5→f(x)=f(-5)=(-5)^3+k(-5)^2+5(-5)-3=-3
Solving for k:
-125+k(25)-25-3=-3
Adding similar terms:
-153+25k=-3
Adding 153 both sides of the equation:
-153+25k+153=-3+153
25k=150
Dividing both sides of the equation by 25:
25k/25=150/25
k=6
