The polynomial generated from the given zeros is: $ P(x) = x^4-50x^3+500x^2+5000x-60000 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -10 $ | $ x+10 $ |
$ 10 $ | $ x-10 $ |
$ 20 $ | $ x-20 $ |
$ 30 $ | $ x-30 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+10 \right) \cdot \left( x-10 \right) \cdot \left( x-20 \right) \cdot \left( x-30 \right) = x^4-50x^3+500x^2+5000x-60000 $$