The polynomial generated from the given zeros is: $ P(x) = 30x^3+7x^2-280x-93 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -3 $ | $ x+3 $ |
$ -\dfrac{ 1 }{ 3 } $ | $ 3x+1 $ |
$ \dfrac{ 31 }{ 10 } $ | $ 10x-31 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+3 \right) \cdot \left( 3x+1 \right) \cdot \left( 10x-31 \right) = 30x^3+7x^2-280x-93 $$