Respuesta :

kudzordzifrancis

Answer:

[tex]p(x)=x^4-x^3+7x^2-9x-18[/tex]

Step-by-step explanation:

The given polynomial has roots 3i, −1, 2

Since [tex]3i[/tex] is a root [tex]-3i[/tex] is also a root.

The factored form of this polynomial is [tex]P(x)=(x-3i)(x+3i)(x+1)(x-2)[/tex]

We need to expand to get:

[tex]p(x)=(x^2-(3i)^2)(x^2-x-2)[/tex]

This becomes [tex]p(x)=(x^2+9)(x^2-x-2)[/tex]

We expand further  to get:

[tex]p(x)=x^4-x^3+7x^2-9x-18[/tex]

The polynomial function is [tex]p (x) = x^4 - x^3 + 7x ^2 - 9x - 18[/tex]

  • The calculation is as follows;

The factored form of the given polynomial should be

[tex]P(x) = (x - 3i) (x + 3i) (x + 1) (x - 2)[/tex]

Now we have to expand it

[tex]p(x) = (x^2 - (3i)^2) (x^2 - x - 2)\\\\= (x^2 + 9) (x^2 - x - 2)[/tex]

[tex]p (x) = x^4 - x^3 + 7x ^2 - 9x - 18[/tex]

Learn more: https://brainly.com/question/24908711?referrer=searchResults

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