The polynomial generated from the given zeros is: $ P(x) = 14x^5+39x^4-67x^3-162x^2+44x+24 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 2 $ | $ x-2 $ |
$ -2 $ | $ x+2 $ |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
$ -\dfrac{ 2 }{ 7 } $ | $ 7x+2 $ |
$ -3 $ | $ x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x+2 \right) \cdot \left( 2x-1 \right) \cdot \left( 7x+2 \right) \cdot \left( x+3 \right) = 14x^5+39x^4-67x^3-162x^2+44x+24 $$