The polynomial generated from the given zeros is: $ P(x) = 2x^4+5x^3-36x^2-41x+70 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -5 $ | $ x+5 $ |
$ -2 $ | $ x+2 $ |
$ 1 $ | $ x-1 $ |
$ \dfrac{ 7 }{ 2 } $ | $ 2x-7 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+5 \right) \cdot \left( x+2 \right) \cdot \left( x-1 \right) \cdot \left( 2x-7 \right) = 2x^4+5x^3-36x^2-41x+70 $$