The polynomial generated from the given zeros is: $ P(x) = 100000x^4-576393x^3-11088856x^2+33204549x+120747780 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -9 $ | $ x+9 $ |
$ -\dfrac{ 223607 }{ 100000 } $ | $ 100000x+223607 $ |
$ 5 $ | $ x-5 $ |
$ 12 $ | $ x-12 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+9 \right) \cdot \left( 100000x+223607 \right) \cdot \left( x-5 \right) \cdot \left( x-12 \right) = 100000x^4-576393x^3-11088856x^2+33204549x+120747780 $$