The polynomial generated from the given zeros is: $ P(x) = 4x^3-9x^2-49x-30 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -2 $ | $ x+2 $ |
$ 5 $ | $ x-5 $ |
$ -\dfrac{ 3 }{ 4 } $ | $ 4x+3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( x+2 \right) \cdot \left( x-5 \right) \cdot \left( 4x+3 \right) = 4x^3-9x^2-49x-30 $$