Question

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

Answer 1

ANSWER

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

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.