Answer:
The polynomial is;
x^4-9x^3+19x^2+9x-20
Step-by-step explanation:
Since it has a degree of 4, the highest power is 4
We have four zeros
So this means that each of the linear factors are;
We get this by equating each of the terms to x
(x-1)(x+1)(x-4)(x-5)
(x-1)(x+1) = x^2-1
So we have
(x-4)(x^2-1)
= x^3-x-4x^2 + 4
And lastly, we have
x(x^3-x-4x^2 + 4)-5(x^3-x-4x^2+4)
So we have;
x^4-x^2-4x^3+4x-5x^3+5x+20x^2-20
x^4-9x^3+19x^2+9x-20
