The polynomial generated from the given zeros is: $ P(x) = x^4+18x^3+121x^2+360x+400 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -5 $ | $ x+5 $ |
$ -5 $ | $ x+5 $ |
$ -4 $ | $ x+4 $ |
$ -4 $ | $ x+4 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+5 \right) \cdot \left( x+5 \right) \cdot \left( x+4 \right) \cdot \left( x+4 \right) = x^4+18x^3+121x^2+360x+400 $$