Answer:
k = 6
Step-by-step explanation:
According to factor/remainder theorem, we will take the value of x which makes 3x-5 equal to 0 and put it into the polynomial and equate it to the remainder.
3x - 5 = 0
3x = 5
x = 5/3
Putting into polynomial:
[tex]3(\frac{5}{3})^3+4(\frac{5}{3})^2+k(\frac{5}{3})+4=39\\3(\frac{125}{27})+4(\frac{25}{9})+\frac{5}{3}k=35\\\frac{125}{9}+\frac{100}{9}+\frac{5}{3}k=35\\\frac{225}{9}+\frac{5}{3}k=35\\\frac{5}{3}k=10\\k=6[/tex]
The value of k is 6
