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.

Expert Answers
Matthew Fonda eNotes educator| Certified Educator

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`

Matthew Fonda eNotes educator| Certified Educator

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-1)(x+2)(x-5)`

`= (x^2 + x - 2)(x - 5)`

`=x^3 - 4x^2 - 7x + 10`

islnds | Student

Yes. Unless you can do it in your head :)

jcjrjamsj | Student

But okay when multiplying them together would you use FOIL on (x-1)(x+2)? And then multiply the answer for that with x-5?

islnds | Student

Let f(x) = (x-5)(x+2)(x-1)