Which of the following is an equation for a polynomial of degree 5 with the following properties:

Question

Zeros only at x=2 and x=−3
f(0)=1296
f(x)<0 only on the interval (2,∞)

f(x)=−12(x+2)^2(x−3)^3
f(x)=12(x−2)^2(x+3)^3
f(x)=27(x−2)^4(x+3)
f(x)=−8(x−2)(x+3)^4
f(x)=−27(x+2)^4(x−3)
f(x)=−216(x−2)(x+3)
f(x)=8(x+2)(x−3)^4
f(x)=18(x+2)^3(x−3)^2

check my answer...I think it is 12(x−2)^2(x+3)^3

thank you

Answer 1

not quite. Your function has f(x) >0 on (2,∞)