The polynomial generated from the given zeros is: $ P(x) = 8x^4+22x^3-57x^2-198x-135 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -\dfrac{ 3 }{ 2 } $ | $ 2x+3 $ |
$ -\dfrac{ 5 }{ 4 } $ | $ 4x+5 $ |
$ -3 $ | $ x+3 $ |
$ 3 $ | $ x-3 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 2x+3 \right) \cdot \left( 4x+5 \right) \cdot \left( x+3 \right) \cdot \left( x-3 \right) = 8x^4+22x^3-57x^2-198x-135 $$