The polynomial generated from the given zeros is: $ P(x) = x^4-1325x^2+122500 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -35 $ | $ x+35 $ |
$ -10 $ | $ x+10 $ |
$ 10 $ | $ x-10 $ |
$ 35 $ | $ x-35 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+35 \right) \cdot \left( x+10 \right) \cdot \left( x-10 \right) \cdot \left( x-35 \right) = x^4-1325x^2+122500 $$