How do you write a polynomial in standard form given the zeros x=1, 2, and 3?

1 Answer
Alan P.
May 12, 2016

The simplest such polynomial would be #color(blue)(x^3-6x^2+11x-6)#

Explanation:

If #1, 2, and 3# are zeros of the polynomial then the polynomial must contain (at least) factors:
#color(white)("XXX")(x-1)#
#color(white)("XXX")(x-2)# and
#color(white)("XXX")(x-3)#

If these are the only factors then our polynomial is
#color(white)("XXX")(x-1)(x-2)(x-3)#

To express this in standard form we need to expand by multiplying and make sure that the terms are listed in descending degree.

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