ANSWER
[tex]f(x) = {x}^{3} + 6 {x}^{2} - 19 - 24[/tex]
EXPLANATION
The polynomial function has zeros at:
-8,-1 and 3
This means the polynomial can be factored as:
[tex]f(x) = (x + 8)(x + 1)(x - 3)[/tex]
We expand the last two factors:
[tex]f(x) = (x + 8)( {x}^{2} - 2x - 3)[/tex]
We expand further to get:
[tex]f(x) = {x}^{3} - 2 {x}^{2} - 3x + 8 {x}^{2} - 16x - 24[/tex]
[tex]f(x) = {x}^{3} + 6 {x}^{2} - 19 - 24[/tex]
The polynomial in descending powers of x is said to be in standard form.
