The polynomial generated from the given zeros is: $ P(x) = x^4+14x^3+65x^2+112x+60 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -1 $ | $ x+1 $ |
$ -5 $ | $ x+5 $ |
$ -2 $ | $ x+2 $ |
$ -6 $ | $ x+6 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+1 \right) \cdot \left( x+5 \right) \cdot \left( x+2 \right) \cdot \left( x+6 \right) = x^4+14x^3+65x^2+112x+60 $$