The polynomial generated from the given zeros is: $ P(x) = 2x^3-15x^2+9x+54 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -\dfrac{ 3 }{ 2 } $ | $ 2x+3 $ |
$ 3 $ | $ x-3 $ |
$ 6 $ | $ x-6 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x+3 \right) \cdot \left( x-3 \right) \cdot \left( x-6 \right) = 2x^3-15x^2+9x+54 $$