The polynomial generated from the given zeros is: $ P(x) = 2x^5+11x^4-3x^3-41x^2+x+30 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
$ -5 $ | $ x+5 $ |
$ 1 $ | $ x-1 $ |
$ -2 $ | $ x+2 $ |
$ -1 $ | $ x+1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-3 \right) \cdot \left( x+5 \right) \cdot \left( x-1 \right) \cdot \left( x+2 \right) \cdot \left( x+1 \right) = 2x^5+11x^4-3x^3-41x^2+x+30 $$