Find the polynomial function with roots 1,-2, and 5.I have looked over the problem 100 times and maybe it's just I overlook everything.
We are looking for a polynomial with roots 1, -2, and 5. If we find functions with each of these as roots, and multiply them together, then the resulting function will have all three as roots. This leads us to the answer:
`f(x) = (x -1)(x + 2)(x - 5)`
If we multiply this out, we get
`f(x) = x^3 - 4x^2 - 7x + 10`
Multiplication is associative, which means that the order in which you do the multplication does not matter--the result will be the same no matter what order you multilply.
So you are correct:
`= (x^2 + x - 2)(x - 5)`
`=x^3 - 4x^2 - 7x + 10`