The polynomial generated from the given zeros is: $ P(x) = 21x^5+62x^4-89x^3-254x^2+20x+24 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ 2 $ | $ x-2 $ |
$ -2 $ | $ x+2 $ |
$ \dfrac{ 1 }{ 3 } $ | $ 3x-1 $ |
$ -\dfrac{ 2 }{ 7 } $ | $ 7x+2 $ |
$ -3 $ | $ x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x-2 \right) \cdot \left( x+2 \right) \cdot \left( 3x-1 \right) \cdot \left( 7x+2 \right) \cdot \left( x+3 \right) = 21x^5+62x^4-89x^3-254x^2+20x+24 $$