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

1 Answer

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

Desmos.comDesmos.com

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