Question

The polynomial px has zeroes at 0 2 and 3-I. The leading coefficient of px is 5 and the zero at 2 has a multiplicity of 3. Write with lowest degree as a product of linear factors with complex coefficients

Answer 1

given a set of zeros: {z1,z2,z3,z4,...,zn}

a polynomial can be defined by the product of linear factors constructed from the zeros

(x-z1)(x-z2)(x-z3)(x-z4)...(x-zn)

if we want to have a leading coeff; stick it out front

a(x-z1)(x-z2)(x-z3)(x-z4)...(x-zn)

Answer 2

keep in mind that complex zeros come in conjugate pairs: a+bi, a-bi

it asks for a mulltiplicity of one of the zeros which can either be stated as: (x-z)^m or (x-z)(x-z)(m-z)...(x-z), for m times