The polynomial generated from the given zeros is: $ P(x) = 2x^3-11x^2+8x+21 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -1 $ | $ x+1 $ |
$ 3 $ | $ x-3 $ |
$ \dfrac{ 7 }{ 2 } $ | $ 2x-7 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x-3 \right) \cdot \left( 2x-7 \right) = 2x^3-11x^2+8x+21 $$