Question

How do you write a polynomial function of least degree with integral coefficients that has the given zeros 3, 2, -1?

Answer 1

`y=(x-3)(x-2)(x+1)`
Also
`y=x^3-4x^2+x+6`

Explanation:

From the given zeros 3, 2, -1

We set up equations `x=3` and `x=2` and `x=-1`. Use all these as factors equal to the variable y.

Let the factors be `x-3=0` and `x-2=0` and `x+1=0`

`y=(x-3)(x-2)(x+1)`

Expanding

`y=(x^2-5x+6)(x+1)`
`y=(x^3-5x^2+6x+x^2-5x+6)`
`y=x^3-4x^2+x+6`

Kindly see the graph of `y=x^3-4x^2+x+6` with zeros at `x=3` and `x=2` and `x=-1`

God bless....I hope the explanation is useful.