The polynomial generated from the given zeros is: $ P(x) = x^4-85x^3+2150x^2-11000x-120000 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -5 $ | $ x+5 $ |
$ 20 $ | $ x-20 $ |
$ 30 $ | $ x-30 $ |
$ 40 $ | $ x-40 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+5 \right) \cdot \left( x-20 \right) \cdot \left( x-30 \right) \cdot \left( x-40 \right) = x^4-85x^3+2150x^2-11000x-120000 $$