write a polynomial in standard for given the zeros; -3, multiplicity 2;2i; degree4

Question

College algebra question

Answer 1

Polynomial must contain (x+3)², x-2i. We need a complement of x-2i, which is x+2i so the product of these complex factors is x²+4. One example is (x+3)²(x²+4) which expands to:

(x²+6x+9)(x²+4)=

x⁴+6x³+9x²+4x²+24x+36=

x⁴+6x³+13x²+24x+36, and any multiple of this.