The polynomial generated from the given zeros is: $ P(x) = x^4+10x^3+7x^2-18x $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -2 $ | $ x+2 $ |
$ -9 $ | $ x+9 $ |
$ 1 $ | $ x-1 $ |
$ 0 $ | $ x $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot \left( x+9 \right) \cdot \left( x-1 \right) \cdot x = x^4+10x^3+7x^2-18x $$