Answer:
The answer is x³-x²-26x-24
Step-by-step explanation:
Firstly, any polynomial can be formed from its roots following the next rule:
Let r1, r2, r3,..., the roots of a polynomial P(x)
P(x)=C*(x-r1)*(x-r2)*(x-r3)*...
Where C is a real constant number excepting zero.
So for roots -4,-1 and 6, the polynomial is:
![C*(x-(-4))*(x-(-1))*(x-6)](https://tex.z-dn.net/?f=C%2A%28x-%28-4%29%29%2A%28x-%28-1%29%29%2A%28x-6%29)
![C*(x+4)*(x+1)*(x-6)\\C*[(x^2+5*x+4)*(x-6)]\\C*[x^3+5*x^2+4*x-6*x^2-30*x-24]\\C*[x^3-x^2-26*x-24]\\](https://tex.z-dn.net/?f=C%2A%28x%2B4%29%2A%28x%2B1%29%2A%28x-6%29%5C%5CC%2A%5B%28x%5E2%2B5%2Ax%2B4%29%2A%28x-6%29%5D%5C%5CC%2A%5Bx%5E3%2B5%2Ax%5E2%2B4%2Ax-6%2Ax%5E2-30%2Ax-24%5D%5C%5CC%2A%5Bx%5E3-x%5E2-26%2Ax-24%5D%5C%5C)
Finally, considering C=1 (can be any real number excepting zero)
![x^3-x^2-26*x-24](https://tex.z-dn.net/?f=x%5E3-x%5E2-26%2Ax-24)