The polynomial generated from the given zeros is: $ P(x) = x^4-28x^3+185x^2-266x $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 7 $ | $ x-7 $ |
$ 2 $ | $ x-2 $ |
$ 0 $ | $ x $ |
$ 19 $ | $ x-19 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-7 \right) \cdot \left( x-2 \right) \cdot x \cdot \left( x-19 \right) = x^4-28x^3+185x^2-266x $$