FUNCTIONS EQUATIONS: algebra 2?

Question

Given the polynomial function h(x)=f(x) times g(x) and
h(2t^3)= 64t^12 - 24t^9 + 104t^6 - 36t^3 + 12.

find g(x) if f(x)=4x^2-3x+2.

Much appreciation.

Answer 1

h(2t^3)= 64t^12 - 24t^9 + 104t^6 - 36t^3 + 12
h(2t^3)=4(2t^3)^4-3(2t^3)3+26(2t^3)2-18(2t^3)+12
Let say x=2t^3
h(x)=4x^4 - 3x^3 + 26x^2 - 18x + 12
f(x)=4x^2 - 3x + 2

h(x)=f(x)*g(x)
g(x)=h(x)/f(x)

g(x)=(4x^4-3x^3+26x^2-18x+12)
/(4x^2-3x+2)

g(x) = x^2+6