Find a degree 3 polynomial with real coefficients having zeros 2 and 3i and a lead coefficient of 1. Write P in expanded form. Be sure to write the full equation including
P(x)=

A degree 3 polynomial with real coefficients having zeros 2 and 3i and a lead coefficient of 1 is

Given :

zeros of polynomial are  2 and 3i and a lead coefficient of 1.

zeros of polynomial are occurs in pairs

3i is one of the zero . Another zero is -3i

So zeros are 2,3i,-3i

Now we write the zeros in factor form

If 'a' is a zero then (x-a) is a factor

zeros are 2,3i,-3i

the factor form is

Now we multiply it to get the polynomial

The polynomial P(x) can be written as

where 'a' is the leading coefficient

we know that leading coefficient is 1

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f(x)=x³-2x²+9x-18

Step-by-step explanation:

complex zeros always occur in pairs.

zeros are 2,3i,-3i

f(x)=(x-2)(x-3i)(x+3i)=(x-2)((x)^2-(3i)^2)

=(x-2)(x^2-9i^2)

=(x-2)(x^2+9)

=x^3-2x^2+9x-18