The polynomial generated from the given zeros is: $ P(x) = x^5-18x^4-2x^3+36x^2+x-18 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 1 $ | $ x-1 $ |
$ -1 $ | $ x+1 $ |
$ 1 $ | $ x-1 $ |
$ -1 $ | $ x+1 $ |
$ 18 $ | $ x-18 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-1 \right) \cdot \left( x+1 \right) \cdot \left( x-1 \right) \cdot \left( x+1 \right) \cdot \left( x-18 \right) = x^5-18x^4-2x^3+36x^2+x-18 $$