The polynomial generated from the given zeros is: $ P(x) = x^4-1300x^3+627500x^2-133250000x+10500000000 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 400 $ | $ x-400 $ |
$ 350 $ | $ x-350 $ |
$ 300 $ | $ x-300 $ |
$ 250 $ | $ x-250 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-400 \right) \cdot \left( x-350 \right) \cdot \left( x-300 \right) \cdot \left( x-250 \right) = x^4-1300x^3+627500x^2-133250000x+10500000000 $$