Question

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

Polynomial of lowest degree with zeros of - 4 (multiplety 1), 3 (multiplicly 3), and with f(0)= 216,

Answer 1

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

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=-(216)/(108)=-2`

So the solution is

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

hope this helps