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Which of the following is a polynomial function in standard form with zeros at -8,-1 and 3? Help needed!!! 10 points!!! Math 3

Which of the following is a polynomial function in standard form with zeros at -8,-1 and-example-1

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ANSWER


f(x) = {x}^(3) + 6 {x}^(2) - 19 - 24

Step-by-step explanation

The polynomial function has zeros at:

-8,-1 and 3

This means the polynomial can be factored as:


f(x) = (x + 8)(x + 1)(x - 3)

We expand the last two factors:


f(x) = (x + 8)( {x}^(2) - 2x - 3)

We expand further to get:


f(x) = {x}^(3) - 2 {x}^(2) - 3x + 8 {x}^(2) - 16x - 24


f(x) = {x}^(3) + 6 {x}^(2) - 19 - 24

The polynomial in descending powers of x is said to be in standard form.

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