The polynomial generated from the given zeros is: $ P(x) = x^3+10x^2+31x+30 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -5 $ | $ x+5 $ |
$ -3 $ | $ x+3 $ |
$ -2 $ | $ x+2 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+5 \right) \cdot \left( x+3 \right) \cdot \left( x+2 \right) = x^3+10x^2+31x+30 $$