How do you write a polynomial in standard form given zeros 4i,4, and -4i?

1 Answer
Mar 16, 2016

Answer:

Start from factored form to find that one such polynomial is

#x^3-4x^2+16x-64#

Explanation:

To create a polynomial with a given set of zeros, we can use the fact that #a# is a zero of a polynomial if and only if #(x-a)# is a factor of the polynomial. Then, starting from the zeros, we can simply take the product of all such factors.

#(x-4)(x-4i)(x-(-4i)) = (x-4)(x-4i)(x+4i)#

#=(x-4)(x^2+16)#

#=x^3-4x^2+16x-64#