# How do you find a polynomial function with zeroes 3,-2,1?

The polynomial is: ${x}^{3} - 2 {x}^{2} - 5 x + 6$
When a number $a$ is a zero of a polynomial, then this polynomial is divisible by $\left(x - a\right)$, so to find the polynomial with zeros $- 2 , 1 , 3$ you have to multiply $\left(x + 2\right) \left(x - 1\right) \left(x - 3\right)$
$\left(x + 2\right) \left(x - 1\right) \left(x - 3\right) = \left({x}^{2} + x - 2\right) \cdot \left(x - 3\right) = {x}^{3} + {x}^{2} - 2 x - 3 {x}^{2} - 3 x + 6 = {x}^{3} - 2 {x}^{2} - 5 x + 6$