The polynomial generated from the given zeros is: $ P(x) = 6x^3-x^2-5x+2 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
$ -1 $ | $ x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 3x-2 \right) \cdot \left( 2x-1 \right) \cdot \left( x+1 \right) = 6x^3-x^2-5x+2 $$