How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are -6, 3, 5?

1 Answer
Jul 24, 2016

Answer:

#f(x) = (x+6)(x-3)(x-5) = x^3-2x^2-33x+90#

Explanation:

For each zero #a#, the polynomial must have a corresponding linear factor #(x-a)#.

So the polynomial of least degree with all three zeros is:

#f(x) = (x+6)(x-3)(x-5) = x^3-2x^2-33x+90#

Any polynomial in #x# with these zeros is a multiple (scalar or polynomial) of this #f(x)#.