The polynomial generated from the given zeros is: $ P(x) = 8x^3+60x^2+150x+125 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
$ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
$ -\dfrac{ 5 }{ 2 } $ | $ 2x+5 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x+5 \right) \cdot \left( 2x+5 \right) \cdot \left( 2x+5 \right) = 8x^3+60x^2+150x+125 $$