The polynomial generated from the given zeros is: $ P(x) = 2x^4+9x^3-19x-12 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -1 $ | $ x+1 $ |
$ -1 $ | $ x+1 $ |
$ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
$ -4 $ | $ x+4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x+1 \right) \cdot \left( 2x-3 \right) \cdot \left( x+4 \right) = 2x^4+9x^3-19x-12 $$