Question

Write a polynomial f(x)that satisfies the given conditions,

Answer 1

Answer:

$\boxed{\sf \ \ \ -2(x+4)(x-3)^3 \ \ \ }$

Step-by-step explanation:

Hello,

let's note k a real, we can write the polynomial as

$k(x-(-4))^1(x-3)^3=k(x+4)(x-3)^3$

and we know that f(0)=216 so

$216=k(0+4)(0-3)^3=k*4*(-1)^3*3^3=-27*4*k=-108k\\\\ k=-\dfrac{216}{108}=-2$

So the solution is

$-2(x+4)(x-3)^3$

hope this helps