The polynomial generated from the given zeros is: $ P(x) = 24x^6-4x^5-194x^4-3x^3+335x^2+67x-105 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ \dfrac{ 3 }{ 2 } $ | $ 2x-3 $ |
$ -1 $ | $ x+1 $ |
$ -\dfrac{ 7 }{ 3 } $ | $ 3x+7 $ |
$ \dfrac{ 5 }{ 2 } $ | $ 2x-5 $ |
$ -1 $ | $ x+1 $ |
$ \dfrac{ 1 }{ 2 } $ | $ 2x-1 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x-3 \right) \cdot \left( x+1 \right) \cdot \left( 3x+7 \right) \cdot \left( 2x-5 \right) \cdot \left( x+1 \right) \cdot \left( 2x-1 \right) = 24x^6-4x^5-194x^4-3x^3+335x^2+67x-105 $$