Explanation
Answer:
Part A
Step 1: Start with the factored form of a polynomial
[tex]\left(\right)=\left(−_1\right)(x-z_2)....(x-z_n)[/tex]Step 2: Insert the given zeros and simplify.
Step 3: Multiply the factored terms together.
Step 4: The answer can be left with the generic “”, or a value for “”can be chosen, inserted, and distributed. In most cases, this is the leading coefficient of the polynomial.
Part B: Given a polynomial of degree 3 with a leading coefficient of 3 and zeros -2 and 5i we can use the above method to get;
[tex]P(x)=3(x-(2)(x-5i)(x-z_3)[/tex]since 5i represents a complex number, there must be a conjugate zero -5i to complement it
Therefore;
[tex]\begin{gathered} P(x)=3(x+2)(x-5i)(x-(-5i)) \\ P(x)=3(x+2)(x-5\imaginaryI)(x+5\imaginaryI) \end{gathered}[/tex]Answer:
[tex]P(x)=3(x+2)(x-5\imaginaryI)(x+5\imaginaryI)[/tex]