Question

Question #e1c6e

Answer 1

If `z` is a zero of polynomial `P`, then `x-z` is a factor of `P`.

So the factors of the desired polynomial must include

`(x+6)(x+1)x(x-1)(x-6)`.

We can put a constant factor in as well.
If the list provided only names and does not count zeros, then we could also raise the factors given to powers greater than `1`.

If you are required to write the polynomial in standard form, I think you'll find it less cumbersome to multiply in a different order than the one above.

`(x+6)(x+1)x(x-1)(x-6) = x[(x+1)(x-1)][(x+6)(x-6)]`.

`= x(x^2-1)(x^2-36)`

`= 1(x^4-37x^2+36)`

`= x^5-27x^3+36x`