2x^3+b*x^2+3x-5 & x^3+x^2-4x+b need the same divider when divided by x-2 find the value of b
f(x) = 2x^3+b*x^2+3x-5
g(x) = x^3+x^2-4x+b
f(2) = 16 + 4b + 6 - 5 = 4b + 17
g(2) = 8 + 4 - 8 + b = b + 4
"need the same divider when divided by x-2 "
----> I don't understand what that means.
Are you saying they have the same remainder?
If so, then
4b+17 = b+4
3b = -13
b = -13/4