The polynomial generated from the given zeros is: $ P(x) = 8x^3+18x^2+3x-2 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ \dfrac{ 1 }{ 4 } $ | $ 4x-1 $ |
$ -\dfrac{ 1 }{ 2 } $ | $ 2x+1 $ |
$ -2 $ | $ x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 4x-1 \right) \cdot \left( 2x+1 \right) \cdot \left( x+2 \right) = 8x^3+18x^2+3x-2 $$