The polynomial generated from the given zeros is: $ P(x) = 625x^4+8875x^3+46925x^2+109445x+94962 $
Step 1: Turn the zeros into factors:
Zero | Factor |
$ -\dfrac{ 14 }{ 5 } $ | $ 5x+14 $ |
$ -\dfrac{ 17 }{ 5 } $ | $ 5x+17 $ |
$ -\dfrac{ 19 }{ 5 } $ | $ 5x+19 $ |
$ -\dfrac{ 21 }{ 5 } $ | $ 5x+21 $ |
Step 2: Multiply the factors together:
$$ P(x) = \left( 5x+14 \right) \cdot \left( 5x+17 \right) \cdot \left( 5x+19 \right) \cdot \left( 5x+21 \right) = 625x^4+8875x^3+46925x^2+109445x+94962 $$