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

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Answer 1 · 2016-07-18T05:32:02

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

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.com

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