Question

explain in words how to find a polynomial in factored form then find a polynomial in factored form of degree 3 with a leading coefficient of 3 and zeros -2 and 5i don't simplify

Answer 1

Step-by-step explanation

Answer:

Part A

Step 1: Start with the factored form of a polynomial

`\left(\right)=\left(−_1\right)(x-z_2)....(x-z_n)`

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;

`P(x)=3(x-(2)(x-5i)(x-z_3)`

since 5i represents a complex number, there must be a conjugate zero -5i to complement it

Therefore;

`\begin{gathered} P(x)=3(x+2)(x-5i)(x-(-5i)) \\ P(x)=3(x+2)(x-5\imaginaryI)(x+5\imaginaryI) \end{gathered}`

Answer:

`P(x)=3(x+2)(x-5\imaginaryI)(x+5\imaginaryI)`