The polynomial generated from the given zeros is: $ P(x) = 2x^3+9x^2-15x-50 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -2 $ | $ x+2 $ |
$ \dfrac{ 5 }{ 2 } $ | $ 2x-5 $ |
$ -5 $ | $ x+5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot \left( 2x-5 \right) \cdot \left( x+5 \right) = 2x^3+9x^2-15x-50 $$