The polynomial generated from the given zeros is: $ P(x) = 1000x^5-18141x^4+112115x^3-309165x^2+383805x-169614 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 9 $ | $ x-9 $ |
$ 3 $ | $ x-3 $ |
$ 2 $ | $ x-2 $ |
$ 1 $ | $ x-1 $ |
$ \dfrac{ 3141 }{ 1000 } $ | $ 1000x-3141 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-9 \right) \cdot \left( x-3 \right) \cdot \left( x-2 \right) \cdot \left( x-1 \right) \cdot \left( 1000x-3141 \right) = 1000x^5-18141x^4+112115x^3-309165x^2+383805x-169614 $$