How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 3, -3, 1?

1 Answer
Alan P.
Nov 9, 2016

#color(green)(f(x)=x^3-x^2-9x+9)#

Explanation:

If the polynomial has zeros at #3, -3, and 1#
then it has factors:
#color(white)("XXX")(x-3), (x+3), and (x-1)#

As a minimal degree polynomial (with leading coefficient #1#)
#color(white)("XXX")(x-3) * (x+3) * (x-1)#

#color(white)("XXX")=(x^2-9) * (x-1)#

#color(white)("XXX")=x^3-x^2-9x+9#

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