The polynomial generated from the given zeros is: $ P(x) = x^5-16x^4+70x^3-48x^2-135x $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 0 $ | $ x $ |
$ 3 $ | $ x-3 $ |
$ 5 $ | $ x-5 $ |
$ -1 $ | $ x+1 $ |
$ 9 $ | $ x-9 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x-3 \right) \cdot \left( x-5 \right) \cdot \left( x+1 \right) \cdot \left( x-9 \right) = x^5-16x^4+70x^3-48x^2-135x $$