Answer:
[tex]\boxed{\sf \ \ \ -2(x+4)(x-3)^3 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's note k a real, we can write the polynomial as
[tex]k(x-(-4))^1(x-3)^3=k(x+4)(x-3)^3[/tex]
and we know that f(0)=216 so
[tex]216=k(0+4)(0-3)^3=k*4*(-1)^3*3^3=-27*4*k=-108k\\\\<=> k=-\dfrac{216}{108}=-2[/tex]
So the solution is
[tex]-2(x+4)(x-3)^3[/tex]
hope this helps
