The polynomial generated from the given zeros is: $ P(x) = x^5-x^4-21x^3+x^2+20x $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 0 $ | $ x $ |
$ -4 $ | $ x+4 $ |
$ 5 $ | $ x-5 $ |
$ -1 $ | $ x+1 $ |
$ 1 $ | $ x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = x \cdot \left( x+4 \right) \cdot \left( x-5 \right) \cdot \left( x+1 \right) \cdot \left( x-1 \right) = x^5-x^4-21x^3+x^2+20x $$