The polynomial generated from the given zeros is: $ P(x) = 3x^3-5x^2-34x+24 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -3 $ | $ x+3 $ |
$ \dfrac{ 2 }{ 3 } $ | $ 3x-2 $ |
$ 4 $ | $ x-4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+3 \right) \cdot \left( 3x-2 \right) \cdot \left( x-4 \right) = 3x^3-5x^2-34x+24 $$