The polynomial generated from the given zeros is: $ P(x) = 2x^3-13x^2-23x-8 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 8 $ | $ x-8 $ |
$ -1 $ | $ x+1 $ |
$ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-8 \right) \cdot \left( x+1 \right) \cdot \left( 2x+1 \right) = 2x^3-13x^2-23x-8 $$