The polynomial generated from the given zeros is: $ P(x) = x^4-1111x^3+112110x^2-1111000x+1000000 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 1 $ | $ x-1 $ |
$ 10 $ | $ x-10 $ |
$ 100 $ | $ x-100 $ |
$ 1000 $ | $ x-1000 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x-10 \right) \cdot \left( x-100 \right) \cdot \left( x-1000 \right) = x^4-1111x^3+112110x^2-1111000x+1000000 $$